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The most popular models for the complex phase and time lags in the rapidaperiodic variability of Galactic X-ray binaries are based Comptonization ofsoft seed photons in a hot corona, where small-scale flares are induced byflares of the soft seed photon input (presumably from a cold accretion disc).However, in their original version, these models have neglected the additionalcooling of the coronal plasma due to the increased soft seed photon input, andassumed a static coronal temperature structure. In this paper, ourMonte-Carlo/Fokker-Planck code for time-dependent radiation transfer andelectron energetics is used to simulate the self-consistent coronal response tothe various flaring scenarios that have been suggested to explain phase andtime lags observed in some Galactic X-ray binaries. It is found that thepredictions of models involving slab-coronal geometries are drasticallydifferent from those deduced under the assumption of a static corona. However,with the inclusion of coronal cooling they may even be more successful than intheir original version in explaining some of the observed phase and time lagfeatures. The predictions of the model of inward-drifting density perturbationsin an ADAF-like, two-temperature flow also differ from the static-corona casepreviously investigated, but may be consistent with the alternating phase lagsseen in GRS 1915+105 and XTE J1550-564. Models based on flares of a cool discaround a hot, inner two-temperature flow may be ruled out for most objectswhere significant Fourier-frequency-dependent phase and time lags have beenobserved.Comment: 23 pages, including 8 figures and 2 tables; accepted for publication  in ApJ; extended discussion w.r.t. original versio

Coronal Cooling and Its Signatures in the Rapid Aperiodic Variability of Galactic Black Hole Candidates