  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 depends also
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 PSD 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.
