wind. We do however make assumptions, which are listed below.

The wind dynamics {#sec:winddynamics}
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The most important assumption in our modelling is that we calculate $\dot{M}$ with a pre-described velocity law. To be more precise, we adopt a $\beta$-type velocity law for the accelerating part of the wind: $$\label{eq_betalaw}
v(r)~=~{\mbox{$v_{\infty}$}}~\left(1~-~\frac{R_*}{r}\right)^\beta$$ Below the sonic point, a smooth transition from this velocity structure is made to a velocity that follows from the photospheric density structure. Vink et al. (2000) have shown that for O stars the predicted mass-loss rate is insensitive to the adopted value of $\beta$ in the range of $\beta$ = 0.7 – 1.5. Therefore, we routinely apply a value of $\beta$ = 1 for O stars, which is consistent with the spectral line modelling of these stars (e.g. Puls et al. 1996), as well as with modified CAK theory, where $\beta$ $\simeq$ 0.8 (Pauldrach et al. 1986). There are observational indications that $\beta$ may be significantly larger than 1 for denser winds, at least in the outer regions (e.g. Barlow & Cohen 1977, Antokhin & Cherepaschuk 2001), although this is still under debate (e.g. Ignace et al. 2003). On numerical grounds, Hillier & Miller (1999) proposed a “double” 