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 (Σ_SFR) and the gas surface density (Σ _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 M _sun) 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 SFR per unit time in this model as a function of Σ _g . This is combined with the molecular gas fraction in order to derive the global dependence of Σ_SFR on Σ _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 Σ_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 easily be incorporated into numerical simulations or semi-analytical models of galaxy formation and evolution.