The radiatively driven wind of the primary star in wind-fed X-ray binaries can be suppressed by the X-ray irradiation of the compact secondary star. This causes feedback between the wind and the X-ray luminosity of the compact star. We estimated how the wind velocity on the face-on side of the donor star depends on the spectral state of the high-mass X-ray binary Cygnus X-3. We modeled the supersonic part of the wind by computing the line force (force multiplier) with the Castor, Abbott and Klein formalism and XSTAR physics and by solving the mass conservation and momentum balance equations. We computed the line force locally in the wind considering the radiation fields from both the donor and the compact star in each spectral state. The wind equations were solved at different orbital angles from the line joining the stars and taking the effect of wind clumping into account. Wind-induced accretion luminosities were estimated using the Bondi-Hoyle-Lyttleton formalism and computed wind velocities at the compact star. We found a correlation between the luminosities estimated from the observations for each spectral state of Cyg X-3 and the computed accretion luminosities assuming moderate wind clumping and a low mass of the compact star. For high wind clumping this correlation disappears. We show that soft X-rays (EUV) from the compact star penetrate the wind from the donor star and diminish the line force and consequently the wind velocity on the face-on side. This increases the computed accretion luminosities qualitatively in a similar manner as observed in the spectral evolution of Cyg X-3 for a moderate clumping volume filling factor and a compact star mass of a few (2 - 3) solar masses.
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