Mass-loss predictions for O and B stars as a function of metallicity

We have calculated a grid of massive star wind models and mass-loss rates for a wide range of metal abundances between $1/100 \le Z/Z_{\odot}\le 10$. The calculation of this grid completes the Vink et al. (2000) mass-loss recipe with an additional parameter Z. We have found that the exponent of the power law dependence of mass loss vs. metallicity is constant in the range between 1/30 ≤ $Z/Z_{\odot}$ ≤ 3. The mass-loss rate scales as $\dot{M} \propto Z^{0.85} v_{\infty}^p$ with $p = -1.23$ for stars with $T_{\rm eff}\ga 25 000$ K, and $p = -1.60$ for the B supergiants with $T_{\rm eff}\la 25 000$ K. Taking also into account the metallicity dependence of $v_{\infty}$, using the power law dependence $v_{\infty}\propto Z^{0.13}$ from Leitherer et al. (1992), the overall result of mass loss as a function of metallicity can be represented by $\dot{M} \propto Z^{0.69}$ for stars with $T_{\rm eff}\ga 25 000$ K, and $\dot{M} \propto Z^{0.64}$ for B supergiants with $T_{\rm eff}\la 25 000$ K. Although it is derived that the exponent of the mass loss vs. metallicity dependence is constant over a large range in Z, one should be aware of the presence of bi-stability jumps at specific temperatures. Here the character of the line driving changes drastically due to recombinations of dominant metal species resulting in jumps in the mass loss. We have investigated the physical origins of these jumps and have derived formulae that combine mass loss recipes for both sides of such jumps. As observations of different galaxies show that the ratio Fe/O varies with metallicity, we make a distinction between the metal abundance Z derived on the basis of iron or oxygen lines. Our mass-loss predictions are successful in explaining the observed mass-loss rates for Galactic and Small Magellanic Cloud O-type stars, as well as in predicting the observed Galactic bi-stability jump. Hence, we believe that our predictions are reliable and suggest that our mass-loss recipe be used in future evolutionary calculations of massive stars at different metal abundance. A computer routine to calculate mass loss is publicly available.