Two-component X-ray spectra (soft multicolour black-body and harder power l
aw) are frequently observed from accreting black holes. These components ar
e presumably associated with the different parts of the accretion flow (opt
ically thick and optically thin respectively) in the vicinity of the compac
t source. Most of the aperiodic variability of the X-ray flux on the short
time-scales is associated with the harder component. We suggest that drasti
cally different amplitudes of variability of these two components are simpl
y related to the very different viscous time-scales in the geometrically th
in and geometrically thick parts of the accretion flow.
In the geometrically thin discs, variations of viscosity or mass accretion
rate occurring at large radius from the black hole on the local dynamical o
r thermal time-scales do not cause any significant variations of the mass a
ccretion rate at smaller radii because of a very long diffusion time. Any v
ariations on the time-scales shorter than the diffusion time-scale are effe
ctively dampened. On the contrary such variations can easily survive in the
geometrically thick flows and as a result the mass accretion rate in the i
nnermost region of the flow will reflect modulations of the mass accretion
rate added to the flow at any distance from the black hole. Therefore if pr
imary instabilities operate on the short time-scales then the stability of
the soft component (originating from the geometrically thin and optically t
hick flow) and variability of the hard component (coming from the geometric
ally thick and optically thin flow) are naturally explained.
For Cygnus X-1, the overall shape of the power density spectra (PDS) in the
soft and hard spectral states can be qualitatively explained if the geomet
rically thin disc is sandwiched by the geometrically thick corona extending
in a radial direction up to a large distance from the compact object. In t
he hard state the thin disc is truncated at some distance from the black ho
le followed by the geometrically thick flow. The break in the PDS is then a
ssociated with the characteristic frequencies in the accretion flow at the
thin disc truncation radius.