$^{13}$CO/C$^{18}$O Gradients Across the Disks of Nearby Spiral Galaxies
  We use the IRAM Large Program EMPIRE and new high-resolution ALMA data to
measure 13CO(1-0)/C18O(1-0) intensity ratios across nine nearby spiral
galaxies. These isotopologues of CO are typically optically thin across most of
the area in galaxy disks, and this ratio allows us to gauge their relative
abundance due to chemistry or stellar nucleosynthesis effects. Resolved
13CO/C18O gradients across normal galaxies have been rare due to the faintness
of these lines. We find a mean 13CO/C18O ratio of 6.0$\pm$0.9 for the central
regions of our galaxies. This agrees well with results in the Milky Way, but
differs from results for starburst galaxies (3.4$\pm$0.9) and ultraluminous
infrared galaxies (1.1$\pm$0.4). In our sample, the 13CO/C18O ratio
consistently increases with increasing galactocentric radius and decreases with
increasing star formation rate surface density. These trends qualitatively
agree with expectations for carbon and oxygen isotopic abundance variations due
to stellar nucleosynthesis, with a possible effect of fractionation.
