Mach number of the inflow (solid lines) and outflow (dotted lines) solutions of Eq. (20) with M(τ)≠0. The supersonic part of the inflow solutions is depicted in orange, and the subsonic part is given in blue. In contrast, the supersonic outflow solution is depicted in blue and the subsonic one in orange. The vertical lines in each frame mark the position of the sonic radius. When radiation dominates, the gas will escape from the gravitational potential of the accretor. Upper, middle, and bottom frames: models with f_disc = 0.5, 0.8, and 0.95, respectively (see Table 1).