Power spectra of black holes and neutron stars as a probe of hydrodynamical structure of the source. Diffusion theory and its application to Cyg X-1 and Cyg X-2 X-ray observations

We present a model of Fourier Power Density Spectrum (PDS) formation in accretion powered X-ray binary systems derived from the first principles of the diffusion theory. Timing properties of X-ray emission are considered to be 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. The resulting PDS continuum is a sum of two components, 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 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 physical parameters of the bounded extended medium, diffusion time scale and the dependence law of viscosity vs radius. We apply our model of the PDS to a sample of RXTE and EXOSAT timing data from Cyg X-1 and Cyg X-2 which describes adequately the spectral transitions in these sources.