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.
