Radial profiles of star formation in the far outer regions of galaxy disks

Star formation in galaxies is triggered by a combination of processes, including gravitational instabilities, spiral wave shocks, stellar compression, and turbulence compression. Some of these persist in the far outer regions, where the column density is far below the threshold for instabilities, making the outer disk cutoff somewhat gradual. We show that in a galaxy with a single exponential gas profile the star formation rate can have a double exponential, with a shallow one in the inner part and a steep one in the outer part. Such double exponentials have been observed recently in the broadband intensity profiles of spiral and dwarf irregular galaxies. The break radius in our model occurs slightly outside the threshold for instabilities, provided the Mach number for compressive motions remains of order unity to large radii. The ratio of the break radius to the inner exponential scale length increases for higher surface brightness disks because the unstable part extends farther out. This is also in agreement with observations. Galaxies with extended outer gas disks that fall more slowly than a single exponential, such as 1/R, can have their star formation rate scale approximately as a single exponential with radius, even out to 10 disk scale lengths. H alpha profiles should drop much faster than the star formation rate as a result of the rapidly decreasing ambient density.