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We derive a metallicity dependent relation between the surface density of thestar formation rate (Sigma_{SFR}) and the gas surface density (Sigma_{g}) in afeedback regulated model of star formation in galactic disks. In this model,star formation occurs in gravitationally bound protocluster clumps embedded inlarger giant molecular clouds with the protocluster clump mass functionfollowing a power law function with a slope of -2. Metallicity dependentfeedback is generated by the winds of OB stars (M > 5 Msol) that form in theclumps. The quenching of star formation in clumps of decreasing metallicityoccurs at later epochs due to weaker wind luminosities, thus resulting inhigher final star formation efficiencies (SFE_{exp}). By combining SFE_{exp}with the timescales on which gas expulsion occurs, we derive the metallicitydependent star formation rate per unit time in this model as a function ofSigma_{g}. This is combined with the molecular gas fraction in order to derivethe global dependence of Sigma_{SFR} on Sigma_{g}. The model reproduces verywell the observed star formation laws extending from low gas surface densitiesup to the starburst regime. Furthermore, our results show a dependence of$\Sigma_{SFR}$ on metallicity over the entire range of gas surface densities incontrast to other models, and can also explain part of the scatter in theobservations. We provide a tabulated form of the star formation laws that canbe easily incorporated into numerical simulations or semi-analytical models ofgalaxy formation and evolution.

Feedback Regulated Star Formation: Implications for the Kennicutt-Schmidt Law