We study a large sample of RXTE PCA/HEXTE observations of Cyg X-1. We characterize the spectra by soft and hard X-ray colours (which define the spectral states), and fit them with a physical model of hybrid, thermal/non-thermal Comptonization. We then fit the power spectra by a sum of Lorentzians. We show the resulting correlations between the spectral colour (defining the hard, intermediate and soft spectral states), the Comptonization amplification factor, the fractional Compton reflection strength, and the peak frequency of the Lorentzians. We also calculate the fractional variability (rms) as a function of photon energy. We fit the obtained rms dependencies by physical models of varying accretion rate, a varying soft-photon input from an outer disc to a hot inner plasma, and a varying dissipation rate in a hot corona above a disc.
Cyg X-1 is an archetypical high-mass X-ray binary containing a persistent black-hole source accreting from an OB supergiant. See, e.g., Zió lkowski (2005) for the properties of the binary, and, e.g., Zdziarski & Gierliński (2004) for a review of its spectral and timing properties.
This work is, in some part, an application to Cyg X-1 of the timing and spectral analysis methods developed for the black-hole low-mass Xray binaries XTE J1550-564 and XTE J1650-500 by Gierliński & Zdziarski (2005). An independent analysis of the spectral correlations only in Cyg X-1 is that of Ibragimov et al. (2005). In addition, we fit the power spectra of Cyg X-1 by a sum of Lorentzian components and look for correlations of the frequencies with other parameters. See Axelsson, Borgonovo & Larsson (2005) for another study of that type.
We can distinguish two approaches to studying X-ray data. In the first one, one may study a small selected sample in great detail. The advantage of this approach is the possibility of studying physics of the sources in detail, and to determine their emission mechanisms and geometry. A disadvantage is that it gives little information regarding the source variability, or dynamics. In the second approach, one may study a large sample of observations using approximate methods, e.g., use a colour-colour diagram. Although this is rather phenomenological, it allows us to study the source behaviour over all its states and it gives some indications about the source dynamics.
In the present analysis, we combine these two approaches. We define here a representative sub-sample chosen from the large number > 700 pointed observations of Cyg X-1 by RXTE performed up to 2004. The chosen subsample covers all spectral colours and all types of variability. Then, we fit the selected data in detail by a physical model. We show the data form a well-defined sequence as a function of the spectral state. This allows us to show a number of clear correlations between various fitted parameters.
In Fig. 1(a), we show the positions of all of the considered observations in a hard-soft colour diagram, based on our fits to the RXTE PCA data. The colours are defined as in Done & Gierliński (2003). The soft and hard colours are defined as the ratios of the intrinsic, absorption-corrected, energy fluxes in the energy bands 4-6.4 keV to 3-4 keV, and 9.7-16 keV to 6.4-9.7 keV, respectively. We see that the observations form a straight line on this plot, with relatively little scatter. This allows us to define our spectral-state parameter as the position on this diagram, changing from 0 at the hardest spectra to 1 at the softest spectra. Fig. 1(b) shows the histogram of the observation number vs. the state parameter. We see two peaks corresponding to the hard and soft states.
Then we define our smaller representative sub-sample, containing 33 data sets studied in detail. They are marked on the colour-colour diagram by black circles in Fig. 2(a), and also in Fig. 2(b), which shows the fractional rms variability of the PCA light curves as a function of the state parameter. We see the rms first declines from the hard state toward softer ones, but it increases again in the softest states. See, e.g., Zdziarski & Gierliński (2004 a non-thermal tail. The model is characterized by the two main parameters, the soft (disc) luminosity (or compactness), ℓ s , and the hard (hot plasma) luminosity/compactness, ℓ h . The compactness is defined as usual, ℓ ≃ Lσ T /m e c 3 , where L is the luminosity, σ T is the Thomson cross section and m e is the electron mass. Hereafter, as our main parameter we use the Comptonization amplification factor, i.e., the hard-to-soft ratio, ℓ h /ℓ s , which is closely related to the X-ray (photon) spectral index, Γ. Then, the hard and intermediate states correspond to ℓ h /ℓ s > ∼ 1, and the soft state corresponds to ℓ h /ℓ s < ∼ 1.
Figs. 3(a-f) present six selected representative energy spectra, EF E , in a sequence from the hard to the soft ones. The numbers in each panel give the RXTE observation ID. The red curves show the un-scattered blackbody component. Scattered blackbody photons provide then seeds for Comptonization by the hybrid plasma. The Comptonized component is shown by the blue curves. Then, that emission is Compton reflected from an opticallythick accretion disc (Magdziarz & Zdziarski 1995), which also gives rise to the Fe K line emission, the sums of both are shown by the green curves.
Fig. 4(a) shows the dependence of the fitted Comptonization amplification factor, ℓ h /ℓ s , on the state parameter. We see a very clear anticorrelation, with our hardest spectrum having ℓ h /ℓ s ≃ 10 and the softest one, ℓ h /ℓ s ≃ 0.25. Here, we define the hard state by ℓ h /ℓ s > 3.5, the intermediate state by 1 < ℓ h /ℓ s < 3.5, and the soft state by ℓ h /ℓ s < 1. In addition, we distinguish the soft states with low and high variability, see Fig. 10 as those shown in Fig. 3. Each spectrum is fitted by a nu
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