  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.
