Comparison of hydrodynamically consistent, pure β law profiles with classical PoWR models with hydrostatic profiles. Top panel: velocity profile as a function of the stellar radius. The gray lines indicate the pure theoretical β law profiles with β = 2.9, 3.3, and 3.9 (dot- dashed, dashed, and solid lines, respectively). The bold blue line is the hydrodynamically consistent PoWR^HD model, whereas the green (continuous velocity gradient connection), purple (forced connection at v = 0.5v_sound), and red (forced connection at v = 0.9v_sound) profiles indicate the classical (β law + hydrostatic integration) PoWR models with β = 3.3. The light blue vertical line indicates the critical point of the PoWRHD model. Second panel: same as the top panel but dividing all the velocity profiles by the hydrodynamical solution, and hence highlighting where velocity profiles differ more. Third panel: comparison of the velocity gradient (dv/dr) profiles. Bottom panel: Spectroscopic comparison between the PoWR models (following the same color code). The observed optical spectrum (ESPRESSO; light gray) is also shown for reference.