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The variability of the X-ray emission from active galactic nuclei is oftencharacterized using time lags observed between soft and hard energy bands inthe detector. The time lags are usually computed using the complex crossspectrum, which is based on the Fourier transforms of the hard and soft timeseries data. It has been noted that some active galactic nuclei display softX-ray time lags, in addition to the more ubiquitous hard lags. Hard time lagsare thought to be produced via propagating fluctuations, spatial reverberation,or via the thermal Comptonization of soft seed photons injected into a hotelectron cloud. The physical origin of the soft lags has been a subject ofdebate over the last decade. Currently, the reverberation interpretation isrecognized as a leading theory. In this paper, we explore the alternativepossibility that the soft X-ray time lags result partially from the thermal andbulk Comptonization of monochromatic seed photons, which in the case of thenarrow-line Seyfert 1 galaxy 1H 0707-495, may correlate with fluorescence ofiron L-line emission. In our model, the seed photons are injected into a hot,quasi-spherical corona in the inner region of the accretion flow. We develop anexact, time-dependent analytical model for the thermal and bulk Comptonizationof the seed photons based on a Fourier-transformed radiation transportequation, and we demonstrate that the model successfully reproduces both thehard and soft time lags observed from 1H 0707-495.

An Analytical Fourier-Transformation Model for the Production of Hard and Soft X-Ray Time Lags in AGNs: Application to 1H 0707-495