Dimensionless velocity profile (w) for the case without line force (η = 0). The black solid line corresponds to α = 1, the black dotted line is α = 0.1, and the black dashed line is α = 0.01. The inset shows a zoomed-in image of the region around the sonic point. The light gray horizontal solid line represents the sound speed value (w = 1). The stellar parameters are given at the beginning of Sect. 5.