In wind-powered X-ray binaries, the radiatively driven stellar wind from the primary may be inhibited by the X-ray irradiation. This creates the feedback that limits the X-ray luminosity of the compact secondary. Wind inhibition might be weakened by the effect of small-scale wind inhomogeneities (clumping) possibly affecting the limiting X-ray luminosity. We study the influence of X-ray irradiation on the stellar wind for different radial distributions of clumping. We calculate hot star wind models with external irradiation and clumping using our global wind code. The models are calculated for different parameters of the binary. We determine the parameters for which the X-ray wind ionization leads to a decrease of the radiative force. This causes a decrease of the wind velocity and even of the mass-loss rate in the case of extreme X-ray irradiation. Clumping weakens the effect of X-ray irradiation because it favours recombination and leads to an increase of the wind mass-loss rate. The best match between the models and observed properties of high-mass X-ray binaries (HMXB) is derived with radially variable clumping. We describe the influence of X-ray irradiation on the terminal velocity and on the mass-loss rate in a parametric way. The X-ray luminosities predicted within the Bondi theory agree nicely with observations when accounting for X-ray irradiation. The ionizing feedback regulates the accretion onto the compact companion resulting in a relatively stable X-ray source. The wind-powered accretion model can account for large luminosities in HMXBs only when introducing the ionizing feedback. There are two possible states following from the dependence of X-ray luminosity on the wind terminal velocity and mass-loss rate. One state has low X-ray luminosity and a nearly undisturbed wind, and the second state has high X-ray luminosity and exhibits a strong influence of X-rays on the flow.
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