1999ApJ...512..793H

We exhibit, by compiling all data sets we can acquire, that the Fourier-frequency-dependent, hard X-ray lags, first observed in the analysis of aperiodic variability of the light curves of the black hole candidate Cyg X-1, appear to be a property shared by several other accreting black hole candidate sources and also by the different spectral states of this source. We then present both analytic and numerical models of these time lags resulting by the process of Comptonization in a variety of hot electron configurations. We argue that, under the assumption that the observed spectra are due to Comptonization, the dependence of the lags on the Fourier period provides a means for mapping the spatial density profile of the hot electron plasma, while the period at which the lags eventually level off provides an estimate of the size of the scattering cloud. We further examine the influence of the location and spatial extent of the soft photon source on the form of the resulting lags for a variety of configurations; we conclude that the study of the X-ray hard lags can provide clues about these parameters of the Comptonization process, too. Fits of the existing data with our models indicate that the size of the Comptonizing clouds are quite large in extent (∼1 lt-s) with inferred radial density profiles that are in many instances inconsistent with those of the standard dynamical models, whereas the extent of the source of soft photons appears to be much smaller than those of the hot electrons by roughly 2 orders of magnitude and its location consistent with the center of the hot electron corona.