  The clumping of massive star winds is an established paradigm confirmed by
multiple lines of evidence and supported by stellar wind theory. The purpose of
this paper is to bridge the gap between detailed models of inhomogeneous
stellar winds in single stars and the phenomenological description of donor
winds in supergiant high-mass X-ray binaries (HMXBs). We use results from
time-dependent hydrodynamical models of the instability in the line-driven wind
of a massive supergiant star to derive the time-dependent accretion rate onto a
compact object in the Bondi-Hoyle-Lyttleton approximation. The strong density
and velocity fluctuations in the wind result in strong variability of the
synthetic X-ray light curves. The model predicts a large scale X-ray
variability, up to eight orders of magnitude, on relatively short timescales.
The apparent lack of evidence for such strong variability in the observed HMXBs
indicates that the details of accretion process act to reduce the variability
due to the stellar wind velocity and density jumps. We, also, study the
absorption of X-rays in the clumped stellar wind by means of a 2-D stochastic
wind model and find that absorption of X-rays changes strongly at different
orbital phases. Furthermore, we address the photoionization in the clumped
wind, and show that the degree of ionization is affected by the wind clumping.
A correction factor for the photoionization parameter is derived. It is shown
that the photoionization parameter is reduced by a factor Xi compared to the
smooth wind models with the same mass-loss rate, where Xi is the wind
inhomogeneity parameter. We conclude that wind clumping must also be taken into
account when comparing the observed and model spectra of the photoionized
stellar wind.
