We use hydrodynamical simulations of disk galaxies to study relations between star formation and properties of the molecular interstellar medium ( ISM ) .
We implement a model for the ISM that includes low-temperature ( T < 10 ^ { 4 } K ) cooling , directly ties the star formation rate to the molecular gas density , and accounts for the destruction of \mathrm { H } _ { 2 } 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 \Sigma _ { \mathrm { SFR } } \propto \Sigma _ { \mathrm { H 2 } } ^ { n _ { \mathrm { mol } } } with n _ { \mathrm { mol } } \approx 1.4 independent of galaxy mass , and a total gas surface density – star formation rate relation \Sigma _ { \mathrm { SFR } } \propto \Sigma _ { \mathrm { gas } } ^ { n _ { \mathrm { tot } } } with a power-law index that steepens from n _ { \mathrm { tot } } \sim 2 for large galaxies to n _ { \mathrm { tot } } \gtrsim 4 for small dwarf galaxies .
We show that deviations from the disk-averaged \Sigma _ { \mathrm { SFR } } \propto \Sigma _ { \mathrm { gas } } ^ { 1.4 } correlation determined by ( 69 ) owe primarily to spatial trends in the molecular fraction f _ { \mathrm { H 2 } } 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 time scales in low-mass and low surface brightness galaxies may owe to their small fractions of molecular gas rather than mediation by strong supernovae-driven winds .
Our simulations also reproduce the observed relations between ISM pressure and molecular fraction and between star formation rate , 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 probability distribution function ( 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 PDFs corresponding to individual , approximately isothermal phases .
We also present a simple method to mitigate numerical Jeans fragmentation of dense , cold gas in Smoothed Particle Hydrodynamics codes through the adoption of a density-dependent pressure floor .