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Astron. Astrophys. 334, 201-209 (1998)

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1. Introduction

The X-ray source Cyg X-1 was discovered by a rocket flight in 1964 (Bowyer et al. 1965). In March 1971 the sudden appearance of an accurately locateable radio source coinciding with a change in the luminosity of the X-ray source led to its identification with the O9.7 Iab supergiant HDE 226868 (Hjellming & Wade 1971, Bolton 1972). This star is known as part of a single lined spectroscopic binary system with an orbital period of 5.6 days at a distance of about 2.5 kpc. The X-ray emission of Cyg X-1 is produced by the accretion of material from the supergiant primary onto the compact object. According to Herrero et al. 1995, the most probable masses of the binary partners are 18 [FORMULA] for the primary and 10 [FORMULA] for the compact object, which is one of the most firmly established black hole candidates (BHCs). The accretion process is believed to be fueled by a focused stellar wind from HDE 226868 (Friend & Castor 1982).

During most of the time Cyg X-1 is emitting a non-thermal or hard state spectrum (for the soft state, cf. Cui et al. 1997), which can be described by a power-law with a photon-index [FORMULA] 1.5-1.7, modified by an exponential cutoff with a folding energy of about 150 keV and reprocessing features. This spectral form can be interpreted as being due to an accretion disk corona (ADC) (Dove et al. 1997and references therein).

The short-term variability of the X-ray emission has been studied in order to gain better insight into the physical processes at work near the compact object. Cyg X-1 was the first source for which X-ray variability on timescales [FORMULA] 1 s was detected (Oda et al. 1971). For a long time this variability was suspected to be a special black hole signature, but today we know that X-ray binaries containing a neutron star instead of a black hole can display similar behavior (Stella et al. 1985). Nevertheless, the efforts in trying to identify a BHC by its irregular short-term variability are continuing (van der Klis 1995).

Until now, no special process could be determined that describes all the properties of the observed short-term variability. We define "variability on short timescales" as variability faster than a few 100 s, with emphasis on timescales [FORMULA] 1 s. These rapid fluctuations are usually described in terms of shot noise models. It has become clear, however, that in the framework of applying conventional shot noise models, complex shot profiles or distributions of shot durations and amplitudes have to be assumed to explain the observations (Nolan et al. 1981, Lochner et al. 1991, Negoro et al. 1994). Shot noise processes exhibit a fixed dynamical behavior in the sense that if the shots are given, no new dynamical information is produced during the run of the Poisson distributed point process. Only by the summation of individual shots the temporal correlations in the time series of the process are generated (Sect. 2.3).

We use the alternative method of applying Linear State Space Models (LSSMs) which are based on stochastic processes (i.e. autoregressive (AR) processes, Scargle 1981) to describe the time series variability. In this case the dynamics of the process are produced using a different approach: each value of the time series refers to earlier values, with their temporal correlation being determined by the dynamical parameters of the system (Sect. 3.1).

The time series of a standard shot noise (exponential decay with one relaxation timescale) and an AR process of first order might look very similar, although the underlying processes differ. The similarity in the time domain leads to shot noise and AR processes both exhibiting an exponentially decaying autocorrelation function (König & Timmer 1997). In contrast to the similarity of the time series, however, the theoretical frequency spectra are different (cf. Eq. 4 and 8). Whereas shot noise profiles with varying relaxation timescales have to be added to approximate the observed periodogram (Lochner et al. 1991), only one dynamical AR parameter is needed to reproduce its properties (Sect. 3.3 and  4.1).

We have studied the high time resolution EXOSAT ME lightcurves of Cyg X-1. The data are presented in Sect. 2.1. A commonly used method to analyze X-ray variability is to work in the frequency domain by fitting theoretical power spectra to the periodogram of a lightcurve: The periodogram of Cyg X-1 and the power spectra of the usually applied shot noise models are reviewed in Sect. 2.2 and 2.3, respectively. Our analysis of the lightcurves with LSSMs, however, is not based on fitting the periodogram but on an alternative procedure working in the time domain. Sect. 3 deals with the theory of the LSSM analysis. Our results are presented in Sect. 4, and in Sect. 5 a possible explanation for the derived relaxation timescale is discussed combining the temporal LSSM results and simulations of comptonized radiation using an accretion disk corona model for Cyg X-1.

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© European Southern Observatory (ESO) 1998

Online publication: May 12, 1998