Phase lags and coherence of X-ray variability in black hole candidates

The ``low'' (hard or ``non-thermal'') state of black hole candidates issometimes modelled via an optically thick, hot Compton cloud that obscures asofter input source such as an accretion disk. In these models the observedoutput spectra consist entirely of photons reprocessed by the cloud, making itdifficult to extract information about the input spectra. Recently Miller(1995) has argued that the Fourier phase (or time) lag between hard and softX-ray photons in actuality represents the phase lags intrinsic to the inputsource, modulo a multiplicative factor. The phase lags thus would be a probe ofthe input photon source. In this paper we examine this claim and find that,although true for the limited parameter space considered by Miller, theintrinsic phase lag disappears whenever the output photon energy is muchgreater than the input photon energy. The remaining time lags represent a``shelf'' due to differences between mean diffusion times across the cloud. Aspointed out by Miller, the amplitude of this shelf -- which is present evenwhen the intrinsic time lags remain -- is indicative of the size andtemperature of the Compton cloud and is a function of the two energies beingcompared. However, we find that with previous instruments such as Ginga theshelf, if present, was likely obscured by counting noise. A more sensitivemeasure of Compton cloud parameters may be obtainable from the coherencefunction, which is derived from the amplitude of the Fourier cross powerspectral density. This function has been seen to exponentially decrease at highFourier frequencies in Cygnus X-1. Coherence loss is characteristic of Comptonclouds that undergo large variations of size and/or temperature on time scaleslonger than about 10 seconds. We argue that observing phase lags and coherenceComment: 14 pages, uuencoded postscript, accepted for publication in Monthly Notice