The empirical metallicity dependence of the mass-loss rate of O- and early B-type stars

[Abridged] We present a comprehensive study of the metallicity dependence of the mass-loss rates in stationary stellar winds of hot massive stars. Assuming a power-law dependence of mass loss on metallicity, Mdot \propto Z^{m}, and adopting a theoretical relation between the terminal velocity and metallicity, v_inf \propto Z^{0.13} (Leitherer et al.), we find m = 0.83 +/- 0.16 for non-clumped outflows from an analysis of the wind momentum luminosity relation (WLR) for stars more luminous than 10^{5.2} Lsun. Within the errors, this result agrees with the prediction of m = 0.69 +/- 0.10 from Vink et al. For the high luminosity stars we find the mass loss rates to be greater than the predictions, implying wind clumping factors in their line-forming regions of ~4. For lower luminosity stars, the winds are so weak that their strengths cannot be reliably derived from optical lines, and one must rely on analysis of UV lines. In the low-luminosity domain the Galactic WLR is found to be much steeper than expected from theory, leading to a discrepancy between UV mass-loss rates and the predictions by a factor 100 at luminosities of L ~ 10^{4.75} Lsun, the origin of which is unknown. We emphasize that even if the current mass-loss rates of hot luminous stars are overestimated as a result of wind clumping, the degree of clumping would likely to be independent of metallicity, so the scalings derived in this study are expected to remain correct.