Illustration of different velocity laws. The full black line at radii beyond 8 R_⋆represents the solution of the momentum equation (Eq. (2)) derived for the wind velocity profile of the oxygen-rich AGB star IK Tau (Decin et al. 2010b); for the region between 1–8 R_⋆ a beta-velocity law with β  =  0.5 is used (Decin et al. 2006). The red dashed line illustrates the β-velocity law (Eq. (4)) for β​ = ​0.5, v₀​ = ​2.7 km s⁻¹, v_∞​ = ​17.68 km s⁻¹, and the vertical black dashed line indicates R_dust at 8.6 R_⋆. An almost perfect fit to the velocity as derived from the momentum equation (Eq. (2)) would be obtained for β  =  1. The dotted blue line represents the Keplerian velocity law for material bound to a star of mass 1 M_⊙.