Density profile (top, in units of g cm⁻³) and opacity profile (bottom, in units of cm² g⁻¹) as a functionof radius for the same 15 M_⊙ stellar models with different mass-loss rates and boundary conditions as in Fig. 1. The colours are as in Fig. 1, and the red circles indicate the location of the sonic point and the green dashed line the Eddington opacity (as defined in Eq. (24) in Sect. 4) of the pink dashed model.