Fig. 8.

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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 Rdust 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⊙.
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