Molecular hydrogen and global star formation relations in galaxies

We use hydrodynamical simulations of disk galaxies to study relations between star formation and properties of the molecular ISM. We implement a model for the ISM that includes low-temperature (T < 10⁴ K) cooling, directly ties the SFR to the molecular gas density, and accounts for the destruction of H₂ by an interstellar radiation field from young stars. We demonstrate that the ISM and star formation model simultaneously produces a spatially resolved molecular gas surface density Schmidt-Kennicutt relation of the form Σ_ESFR ∝ Σ_H2 ^nmol with n_mol ≈1.4 independent of galaxy mass, and a total gas surface density-SFR relation Σ_ESFR ∝ Σ_gas^ntot with a power-law index that steepens from n_tot ∼2 for large galaxies to n_tot≳ 4 for small dwarf galaxies. We show that deviations from the disk-averaged Σ_ESFR ∝ Σ_gas^1.4 correlation determined by Kennicutt owe primarily to spatial trends in the molecular fractionf_H2, and may explain observed deviations from the global Schmidt-Kennicutt relation. In our model, such deviations occur in regions of the ISM where the fraction of gas mass in molecular form is declining or significantly less than unity. Long gas consumption timescales in low-mass and low surface brightness galaxies may owe to their small fractions of molecular gas rather than mediation by strong supernova-driven winds. Our simulations also reproduce the observed relations between ISM pressure and molecular fraction and between SFR, gas surface density, and disk angular frequency. We show that the Toomre criterion that accounts for both gas and stellar densities correctly predicts the onset of star formation in our simulated disks. We examine the density and temperature distributions of the ISM in simulated galaxies and show that the density pdf generally exhibits a complicated structure with multiple peaks corresponding to different temperature phases of the gas. The overall density pdf can be well modeled as a sum of lognormal pdf's corresponding to individual, approximately isothermal phases. We also present a simple method to mitigate numerical Jeans fragmentation of dense, cold gas in SPH codes through the adoption of a density-dependent pressure floor.