  The most popular models for the complex phase and time lags in the rapid
aperiodic variability of Galactic X-ray binaries are based Comptonization of
soft seed photons in a hot corona, where small-scale flares are induced by
flares of the soft seed photon input (presumably from a cold accretion disc).
However, in their original version, these models have neglected the additional
cooling of the coronal plasma due to the increased soft seed photon input, and
assumed a static coronal temperature structure. In this paper, our
Monte-Carlo/Fokker-Planck code for time-dependent radiation transfer and
electron energetics is used to simulate the self-consistent coronal response to
the various flaring scenarios that have been suggested to explain phase and
time lags observed in some Galactic X-ray binaries. It is found that the
predictions of models involving slab-coronal geometries are drastically
different from those deduced under the assumption of a static corona. However,
with the inclusion of coronal cooling they may even be more successful than in
their original version in explaining some of the observed phase and time lag
features. The predictions of the model of inward-drifting density perturbations
in an ADAF-like, two-temperature flow also differ from the static-corona case
previously investigated, but may be consistent with the alternating phase lags
seen in GRS 1915+105 and XTE J1550-564. Models based on flares of a cool disc
around a hot, inner two-temperature flow may be ruled out for most objects
where significant Fourier-frequency-dependent phase and time lags have been
observed.
