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Many statistical properties of X-ray aperiodic variability from accretingcompact objects can be explained by the propagating fluctuations model appliedto the accretion disc. The mass accretion rate fluctuations originate fromvariability of viscosity, which arises at every radius and causes localfluctuations of the density. The fluctuations diffuse through the disc andresult in local variability of the mass accretion rate, which modulates theX-ray flux from the inner disc in the case of black holes, or from the surfacein the case of neutron stars. A key role in the theoretical explanation of fastvariability belongs to the description of the diffusion process. Thepropagation and evolution of the fluctuations is described by the diffusionequation, which can be solved by the method of Green functions. We implementGreen functions in order to accurately describe the propagation of fluctuationsin the disc. For the first time we consider both forward and backwardpropagation. We show that (i) viscous diffusion efficiently suppressvariability at time scales shorter than the viscous time, (ii) localfluctuations of viscosity affect the mass accretion rate variability both inthe inner and the outer parts of accretion disc, (iii) propagating fluctuationsgive rise not only to hard time lags as previously shown, but also produce softlags at high frequency similar to those routinely attributed to reprocessing,(iv) deviation from the linear rms-flux relation is predicted for the case ofvery large initial perturbations. Our model naturally predicts bumpy powerspectra.

Propagating mass accretion rate fluctuations in X-ray binaries under the influence of viscous diffusion