Testing the Molecular-Hydrogen Kennicutt-Schmidt Law in the Low-Density
  Environments of Extended Ultraviolet Disk Galaxies
  Studying star formation beyond the optical radius of galaxies allows us to
test empirical relations in extreme conditions with low average gas density and
low molecular fraction. Previous studies discovered galaxies with extended
ultraviolet (XUV) disks, which often contain star forming regions with lower
Halpha-to-far-UV (FUV) flux ratios compared to inner disk star forming regions.
However, most previous studies lack measurements of molecular gas, which is
presumably the component of the interstellar medium out of which stars form. We
analyzed published CO measurements and upper limits for fifteen star forming
regions in the XUV or outer disk of three nearby spiral galaxies and a new CO
upper limit from the IRAM 30 m telescope in one star forming region at r = 3.4
r_25 in the XUV disk of NGC 4625. We found that the star forming regions are in
general consistent with the same molecular-hydrogen Kennicutt-Schmidt law that
applies within the optical radius, independent of whether we used Halpha or FUV
as the star formation rate (SFR) tracer. However, a number of the CO detections
are significantly offset towards higher SFR surface density for their molecular
hydrogen surface density. Deeper CO data may enable us to use the presence or
absence of molecular gas as an evolutionary probe to break the degeneracy
between age and stochastic sampling of the initial mass function as the
explanation for the low Halpha-to-FUV flux ratios in XUV disks.
