  The variability of the X-ray emission from active galactic nuclei is often
characterized using time lags observed between soft and hard energy bands in
the detector. The time lags are usually computed using the complex cross
spectrum, which is based on the Fourier transforms of the hard and soft time
series data. It has been noted that some active galactic nuclei display soft
X-ray time lags, in addition to the more ubiquitous hard lags. Hard time lags
are thought to be produced via propagating fluctuations, spatial reverberation,
or via the thermal Comptonization of soft seed photons injected into a hot
electron cloud. The physical origin of the soft lags has been a subject of
debate over the last decade. Currently, the reverberation interpretation is
recognized as a leading theory. In this paper, we explore the alternative
possibility that the soft X-ray time lags result partially from the thermal and
bulk Comptonization of monochromatic seed photons, which in the case of the
narrow-line Seyfert 1 galaxy 1H 0707-495, may correlate with fluorescence of
iron 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 an
exact, time-dependent analytical model for the thermal and bulk Comptonization
of the seed photons based on a Fourier-transformed radiation transport
equation, and we demonstrate that the model successfully reproduces both the
hard and soft time lags observed from 1H 0707-495.
