REGULATION OF STAR FORMATION RATES IN MULTIPHASE GALACTIC DISKS: A THERMAL/DYNAMICAL EQUILIBRIUM MODEL

We develop a model for the regulation of galactic star formation rates Sigma(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 SSFR as a function of the total gaseous surface density S and the midplane density of stars+dark matter rho(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 SSFR, must adjust until it matches the midplane pressure value set by the vertical gravitational field. Our model applies to regions where Sigma less than or similar to 100 M-circle dot pc(-2). In low-Sigma(SFR) (outer-galaxy) regions where diffuse gas dominates, the theory predicts that Sigma(SFR) alpha Sigma root rho(sd). The decrease of thermal equilibrium pressure when SSFR 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 S. 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.