$\beta$ law, with $\beta_{1} = 1$ for the inner and $\beta_2 = 50$ for the outer wind, which appears to be a good approximation of the self-consistently derived velocity law for the WC5 star modelled by Gräfener & Hamann (2005). Here we do not apply a 2-step velocity law, but we do explore the difference between a “low” value of $\beta$ ($\beta$ = 1), and a larger value ($\beta$ = 3) as to test the sensitivity of the velocity law assumption, and to investigate whether our choice of $\beta$ influences the derived WR wind metallicity dependence significantly. We find that this is not the case (Sect. \[s\_beta\]).

We stress that although our approach allows for a derivation of the mass loss that can be driven by the photons passing through the outer atmosphere, it does not treat the initiation and driving of the wind in the deepest layers at very large optical depth (above a Rosseland optical depth of 30). To do so properly would require (i) taking account of the back-warming of Fe at large depths (as this affects the temperature and ionization structure), (ii) a co-moving frame treatment of the lines (we adopt an improved Sobolev description appropriate 