We use the adaptive mesh refinement code Enzo to model the interstellar medium (ISM) in isolated local disk galaxies. The simulation includes a treatment for star formation and stellar feedback. We get a highly supersonic turbulent disk, which is fragmented at multiple scales and characterized by a multi-phase ISM. We show that a Kennicutt-Schmidt relation only holds when averaging over large scales. However, values of star formation rates and gas surface densities lie close in the plot for any averaging size. This suggests an intrinsic relation between stars and gas at cell-size scales, which dominates over the global dynamical evolution. To investigate this effect, we develop a method to simulate the creation of stars based on the density field from the snapshots, without running the code again. We also investigate how the star formation law is affected by the characteristic star formation timescale, the density threshold, and the efficiency considered in the recipe. We find that the slope of the law varies from ~1.4 for a free-fall timescale, to ~1.0 for a constant depletion timescale. We further demonstrate that a power law is recovered just by assuming that the mass of the new stars is a fraction of the mass of the cell m = ρgasΔx 3, with no other physical criteria required. We show that both efficiency and density threshold do not affect the slope, but the right combination of them can adjust the normalization of the relation, which in turn could explain a possible bi-modality in the law.
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