Star Formation in Isolated Disk Galaxies. II. Schmidt Laws and Efficiency of Gravitational Collapse

(Abridged). We model gravitational instability in a wide range of isolated disk galaxies, using GADGET, a three-dimensional, smoothed particle hydrodynamics code. The model galaxies include a dark matter halo and a disk of stars and isothermal gas. The global Schmidt law observed in disk galaxies is quantitatively reproduced by our models. We find that the surface density of star formation rate directly correlates with the strength of local gravitational instability. The local Schmidt laws of individual galaxies in our models show clear evidence of star formation thresholds. Our results suggest that the non-linear development of gravitational instability determines the local and global Schmidt laws, and the star formation thresholds.