subsequent thermal emission, which are included in our model. This implies that we have a channel to redistribute photons towards longer wavelength, away from the flux maximum, so that we cannot directly compare to these findings. Nonetheless, we anticipate that the neglect of line branching could cause an overprediction of the mass-loss rate by a factor of 1–3 at galactic $Z$. As the importance of line branching is expected to decrease at lower $Z$, we anticipate that by neglecting line branching we may slightly overestimate the exponent in the ${\mbox{$\dot{M}$}}$–$Z$ relation.

Wind clumping {#sec:nowindclumping}
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It has been established that small-scale clumping of the outflowing gas has a pronounced effect on the ionization structure of WR atmospheres, as it favours recombination over ionization processes (e.g. Hillier 1991). In addition, clumping may have a direct effect on the radiative driving, although these effects may be complex and challenging to predict (Schmutz 1997, Hillier 2003). In more quantitative terms, the observed emission line spectrum – formed through recombination – is essentially invariant for the ratio ${\mbox{$\dot{M}$}}/\sqrt{f}$, where $f$ is the volume clumping factor describing the mean density in the flow $\overline{\rho} = f \times \rho$, where $\rho$ is the density in the 