On the X-ray time lags in the black hole candidates

Abstract

It is shown that the energy dependence of the time lags in Cygnus X-1 excludes any significant contribution of the standard reflected component to the observed lags. The conclusion is valid in the 0.1--10 Hz frequency range where time lags have been detected with high enough significance. In fact the data hint that reflected component is working in opposite direction, reducing the lags at energies where contribution of the reflected component is significant. We argue that the observed logarithmic dependence of time lags on energy can be understood as due to the small variations of the spectrum power law index in a very simple phenomenological model. We assume that an optically thin flow/corona, emitting a power law like spectrum, is present at a range of distances from the compact object. The slope of the locally emitted spectrum is a function of distance with the hardest spectrum emitted in the innermost region. If perturbations with different time scales are introduced to the accretion flow at different radii the observed X-ray lags naturally appear due to the inward propagation of perturbations on the diffusion time scales.