2010ApJ...721..975O

We develop a model for the regulation of galactic star formation rates Σ_SFR in disk galaxies, in which interstellar medium (ISM) heating by stellar UV plays a key role. By requiring that thermal and (vertical) dynamical equilibrium are simultaneously satisfied within the diffuse gas, and that stars form at a rate proportional to the mass of the self-gravitating component, we obtain a prediction for Σ_SFR as a function of the total gaseous surface density Σ and the midplane density of stars+dark matter ρ_sd. The physical basis of this relationship is that the thermal pressure in the diffuse ISM, which is proportional to the UV heating rate and therefore to Σ_SFR, must adjust until it matches the midplane pressure value set by the vertical gravitational field. Our model applies to regions where Σ ≲ 100 M_☉pc^–2. In low-Σ_SFR(outer-galaxy) regions where diffuse gas dominates, the theory predicts that Σ_SFR∝Σsqrt(ρ_sd). The decrease of thermal equilibrium pressure when Σ_SFR is low implies, consistent with observations, that star formation can extend (with declining efficiency) to large radii in galaxies, rather than having a sharp cutoff at a fixed value of Σ. The main parameters entering our model are the ratio of thermal pressure to total pressure in the diffuse ISM, the fraction of diffuse gas that is in the warm phase, and the star formation timescale in self-gravitating clouds; all of these are (at least in principle) direct observables. At low surface density, our model depends on the ratio of the mean midplane FUV intensity (or thermal pressure in the diffuse gas) to the star formation rate, which we set based on solar-neighborhood values. We compare our results to recent observations, showing good agreement overall for azimuthally averaged data in a set of spiral galaxies. For the large flocculent spiral galaxies NGC 7331 and NGC 5055, the correspondence between theory and observation is remarkably close.