  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 broad-band 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 further 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. Halpha profiles should drop much faster than
the star formation rate as a result of the rapidly decreasing ambient density.

Astrophysics