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Many accreting black holes manifest time lags during outbursts, in which thehard Fourier component typically lags behind the soft component. Despitedecades of observations of this phenomenon, the underlying physical explanationfor the time lags has remained elusive, although there are suggestions thatCompton reverberation plays an important role. However, the lack of analyticalsolutions has hindered the interpretation of the available data. In this paper,we investigate the generation of X-ray time lags in Compton scattering coronaeusing a new mathematical approach based on analysis of the Fourier-transformedtransport equation. By solving this equation, we obtain the Fourier transformof the radiation Green's function, which allows us to calculate the exactdependence of the time lags on the Fourier frequency, for both homogeneous andinhomogeneous coronal clouds. We use the new formalism to explore a variety ofinjection scenarios, including both monochromatic and broadband(bremsstrahlung) seed photon injection. We show that our model can successfullyreproduce both the observed time lags and the time-averaged (quiescent) X-rayspectra for Cyg~X-1 and GX~339-04, using a single set of coronal parameters foreach source. The time lags are the result of impulsive bremsstrahlung injectionoccurring near the outer edge of the corona, while the time-averaged spectraare the result of continual distributed injection of soft photons throughoutthe cloud.

An Integrated Model for the Production of X-Ray Time Lags and Quiescent Spectra from Homogeneous and Inhomogeneous Black Hole Accretion Coronae