Temporal and spectral properties of comptonized radiation and its applications

We have found relations between the temporal and spectral properties of radiation Comptonized in an extended atmosphere associated with compact accreting sources. We demonstrate that the fluctuation power spectrum density (PSD) imposes constraints on the atmosphere scale and profile. Furthermore, we indicate that the slope and low-frequency break of the PSD are related to the Thomson depth, tau(0), of the atmosphere and the radius of its physical size, respectively. Since the energy spectrum of the escaping radiation also depends on tau(0) (and the electron temperature kT(e)), the relation between spectral and temporal properties follows. This relation allows, for the first time, an estimate of the accreting matter Thomson depth, tau(0), independent of arguments involving Comptonization. We present figures for the light curves and PSDs of different energy bands, the photon energy spectra, and the phase lags as functions of the variability frequency. The temporal properties of the high (soft) and low (hard) state of black hole sources are discussed in this context.