Star Formation Thresholds and Galaxy Edges: Why and Where

Disk galaxies have fairly sharp edges: both the star formation rate and the stellar surface density cut off beyond a few disk scale lengths. The existence of a surface density threshold for star formation is usually explained in terms of the Toomre criterion for gravitational instability in a thin, rotating disk. Here it is shown that it is not gravitational instability that causes the formation of a cold, molecular phase, but vice versa: the transition from the warm (T ~ 10⁴ K) to the cold (T < 10³ K) interstellar phase causes the disk to become gravitationally unstable. Rotation does not affect the critical surface density at which the phase transition occurs and cannot stabilize the cold phase in the outer disk. Models based on the hypothesis that the onset of thermal instability determines the star formation threshold reproduce the observed threshold radii and column densities. Beyond the threshold radius the fraction of the gas in molecular form is predicted to decline rapidly, in agreement with observations. The model can also account for the observed 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.