An Integrated Model for the Production of X-Ray Time Lags and Quiescent   Spectra from Homogeneous and Inhomogeneous Black Hole Accretion Coronae
  Many accreting black holes manifest time lags during outbursts, in which the hard Fourier component typically lags behind the soft component. Despite decades of observations of this phenomenon, the underlying physical explanation for the time lags has remained elusive, although there are suggestions that Compton reverberation plays an important role. However, the lack of analytical solutions has hindered the interpretation of the available data. In this paper, we investigate the generation of X-ray time lags in Compton scattering coronae using a new mathematical approach based on analysis of the Fourier-transformed transport equation. By solving this equation, we obtain the Fourier transform of the radiation Green's function, which allows us to calculate the exact dependence of the time lags on the Fourier frequency, for both homogeneous and inhomogeneous coronal clouds. We use the new formalism to explore a variety of injection scenarios, including both monochromatic and broadband (bremsstrahlung) seed photon injection. We show that our model can successfully reproduce both the observed time lags and the time-averaged (quiescent) X-ray spectra for Cyg~X-1 and GX~339-04, using a single set of coronal parameters for each source. The time lags are the result of impulsive bremsstrahlung injection occurring near the outer edge of the corona, while the time-averaged spectra are the result of continual distributed injection of soft photons throughout the cloud. 
John J. Kroon, Peter A. Becker
astro-ph.HE