An Analytical Fourier-Transformation Model for the Production of X-ray Time Lags from AGN Accretion Disks

The complex and rapid variability of X-ray emissions from active galactic nuclei (AGNs) provides insights into the detailed thermal and dynamical structure of the inner region of the accretion disk around the central black hole. One way to analyze the observed variability is via Fourier time lags which are the temporal lags between Fourier transforms of light curves at different (e.g. hard or soft) X-ray energy channels. These observed X-ray time lags can be either hard lags or soft lags depending on whether the variability in the hard X-ray energy channel lags behind that in the soft X-ray channel or vice versa. The physical explanation for the time lags from AGNs has been an active topic, and several scenarios have been proposed. In this study, we explore the hypothesis that the production of X-ray time lags is a combined result of thermal and bulk Comptonization and spatial reverberation of iron L-line and K-line seed photons generated via fluorescence, which is driven by a variable incident radiation field. We approximate that the inner region of the accretion disk is self-similar ADAF, with half-thickness ∝ , where is the radius from the central black hole. A Fourier-transformed, vertically-averaged transport equation in cylindrical coordinates is used to analyze the time-dependent radiative transfer in the disk and to predict the observed data. We demonstrate that our model can successfully reproduce the X-ray time lags for the Seyfert 1 galaxies 1H 0707-495 and Ark 564.