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

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