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

Many statistical properties of X-ray aperiodic variability from accreting compact objects can be explained by the propagating fluctuations model applied to the accretion disc. The mass accretion rate fluctuations originate from variability of viscosity, which arises at every radius and causes local fluctuations of the density. The fluctuations diffuse through the disc and result in local variability of the mass accretion rate, which modulates the X-ray flux from the inner disc in the case of black holes, or from the surface in the case of neutron stars. A key role in the theoretical explanation of fast variability belongs to the description of the diffusion process. The propagation and evolution of the fluctuations is described by the diffusion equation, which can be solved by the method of Green functions. We implement Green functions in order to accurately describe the propagation of fluctuations in the disc. For the first time we consider both forward and backward propagation. We show that (i) viscous diffusion efficiently suppresses variability at time-scales shorter than the viscous time; (ii) local fluctuations of viscosity affect the mass accretion rate variability both in the inner and the outer parts of accretion disc; (iii) propagating fluctuations give rise not only to hard time lags as previously shown, but also produce soft lags at high frequency similar to those routinely attributed to reprocessing and (iv) deviation from the linear rms-flux relation is predicted for the case of very large initial perturbations. Our model naturally predicts bumpy power spectra.