Phase Lags and Coherence of X-ray Variability in Black Hole Candidates

The \low" (hard or \non-thermal") state of black hole candidates is sometimes modelled via an optically thick, hot Compton cloud that obscures a softer input source such as an accretion disk. In these models the observed output spectra consist entirely of photons reprocessed by the cloud, making it diicult to extract information about the input spectra. Recently Miller (1995) has argued that the Fourier phase (or time) lag between hard and soft X-ray photons in actuality represents the phase lags intrinsic to the input source, modulo a multiplicative factor. The phase lags thus would be a probe of the input photon source. In this paper we examine this claim and nd that, although true for the limited parameter space considered by Miller, the intrinsic phase lag disappears whenever the output photon energy is much greater than the input photon energy. The remaining time lags represent a \shelf" due to diierences between mean diiusion times across the cloud. As pointed out by Miller, the amplitude of this shelf { which is present even when the intrinsic time lags remain { is indicative of the size and temperature of the Compton cloud and is a function of the two energies being compared. However, we nd that with previous instruments such as Ginga the shelf, if present, was likely obscured by counting noise. A more sensitive measure of Compton cloud parameters may be obtainable from the coherence function, which is derived from the amplitude of the Fourier cross power spectral density. This function has been seen to exponentially decrease at high Fourier frequencies in Cygnus X-1. Coherence loss is characteristic of Compton clouds that undergo large variations of size and/or temperature on time scales longer than about 10 seconds. We argue that observing phase lags and coherence at a variety of energies and Fourier frequencies is more likely to reveal information about the nature of Compton clouds, rather than about their soft input sources. A number of black hole candidates (BHC) exhibit energy spectra that are well modelled by power laws with photon indexes of < 1:7 between energies of 1 > 100 keV (so-called \low states"). These spectra have been successfully modelled as soft input photons upscattered in an optically thick Compton cloud. The power law spectra is obtained from the fact that although the probability of scattering decreases exponentially with the number of scatters, the energy gain by the photons increases …