On the relation between the Schmidt and Kennicutt-Schmidt star formation laws and its implications for numerical simulations

When averaged over large scales, star formation in galaxies is observed to follow the empirical Kennicutt-Schmidt (KS) law for surface densities above a constant threshold. While the observed law involves surface densities, theoretical models and simulations generally work with volume density laws (i.e. Schmidt laws). We derive analytic relations between star formation laws expressed in terms of surface densities, volume densities, and pressures and we show how these relations depend on parameters such as the effective equation of state of the multiphase interstellar medium. Our analytic relations enable us to implement observed surface density laws into simulations. Because the parameters of our prescription…