2007ApJ...660..556T

We present a model of Fourier power density spectrum (PDS) formation in accretion-powered X-ray binary systems derived from diffusion theory. Timing properties of X-ray emission are considered a result of diffusive propagation of the driving perturbations in a bounded medium. We prove that the integrated power P_x of the resulting PDS is only a small fraction of the integrated power P_dr of the driving oscillations, which is distributed over the disk. Furthermore, we demonstrate that P_x is inversely proportional to the characteristic frequency of the driving oscillations ν_dr, which likely scales with the frequency of the local gravity waves in the disk (Keplerian frequency). Because ν_dr increases toward soft states, we conclude that P_x declines toward soft states. This dependence P_x∝ν^–1_dr explains the well-known observational phenomenon that the X-ray variability power decreases when the source evolves to softer states. The resulting PDS continuum is a sum of a low-frequency (LF) component, which presumably originates in an extended accretion disk, and a high-frequency (HF) component, which originates in the innermost part of the source (Compton cloud or corona). The LF PDS component has a power-law shape with an index of 1.0-1.5 at higher frequencies (``red'' noise) and a flat spectrum below a characteristic (break) frequency (``white'' noise). This white-red noise (WRN) continuum spectrum holds information about the bounded extended medium, the diffusion timescale, and the dependence law of viscosity versus radius. We apply our model of the PDS to RXTE and EXOSAT timing data from Cygnus X-1 and Cygnus X-2, which describes adequately the spectral transitions in these sources. The presented PDSs are shown in frequency range from 10^–8 to 10² Hz, 10 orders of magnitude.