We study global star formation thresholds in the outer parts of galaxies by investigating the stability of disk galaxies embedded in dark halos. The disks are self-gravitating, contain metals and dust, and are exposed to UV radiation. We find that the critical surface density for the existence of a cold interstellar phase depends only weakly on the parameters of the model and coincides with the empirically derived surface density threshold for star formation. Furthermore, it is shown that the drop in the thermal velocity dispersion associated with the transition from the warm to the cold gas phase triggers gravitational instability on a wide range of scales. The presence of strong turbulence does not undermine this conclusion if the disk is self-gravitating. Models based on the hypothesis that the onset of thermal instability determines the star formation threshold in the outer parts of galaxies can reproduce many observations, including the threshold radii, column densities, and the sizes of stellar disks as a function of disk scale length and mass. Finally, prescriptions are given for implementing star formation thresholds in (semi-)analytic models and three-dimensional hydrodynamical simulations of galaxy formation.
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