Topology of solutions of the equation of motion, Eq. (40), vs. radial distance in units of the critical radius at the pole, for a typical O5–V-star in the centre with the line acceleration parameters ĝ₀ = 17661, γ = 0.4758, δ = 0.6878 and in Eq. (39), according to v_∞ = 3232 km/s. The horizontal line marks the critical velocity (i.e. sound speed v_c = a). Solution 1 is the unique trans-sonic stellar wind solution through the critical point at and . For the description of the different solutions of type 2–6, see the discussion in Sects. 2.6.1 and 2.6.3.