Two-dimensional simulations of the stellar wind in the equatorial plane of Cygnus X-1 including the effects of the X-ray ionization. Panels show the density distribution ρ, the velocity magnitude , and the ionization parameter ξ. α is set to 0.6, and k = k(ξ). The wind launching from the hemisphere facing the X-ray source is noticeably slower than the wind coming from the opposite hemisphere, which lies in the X-ray shadow (the dark cone-like region in the right panels). A strong shock forms in the region where the fast and slow wind collide. The accretion of the slow wind is much more efficient, giving rise to an extensive disk that is enveloped by a strong shock front. In the region where log ξ ≥ 2, the line-driven acceleration mechanism of the material of the wind is switched off, which causes the wind coming from the hemisphere facing the X-ray source to slow down. (This figure is available in colour in the electronic version of the paper.)