The CO-to-H$_2$ Conversion Factor in the Barred Spiral Galaxy M83

We analyze the CO-to-H$_2$ conversion factor ($\alpha_{\rm{CO}}$) in the nearby barred spiral galaxy M83. We present new HI observations from the JVLA and single-dish GBT in the disk of the galaxy, and combine them with maps of CO(1-0) integrated intensity and dust surface density from the literature. $\alpha_{\rm{CO}}$ and the gas-to-dust ratio ($\delta_{\rm{GDR}}$) are simultaneously derived in annuli of 2 kpc width from R = 1-7 kpc. We find that $\alpha_{\rm{CO}}$ and $\delta_{\rm{GDR}}$ both increase radially, by a factor of $\sim$ 2-3 from the center to the outskirts of the disk. The luminosity-weighted averages over the disk are $\alpha_{\rm{CO}} = 3.14$ (2.06, 4.96) M$_{\odot}$ pc$^{-2}$[K$\cdot$ km s$^{-1}$]$^{-1}$ and $\delta_{\rm{GDR}}$ = 137 (111, 182) at the 68% (1$\sigma$) confidence level. These are consistent with the $\alpha_{\rm{CO}}$ and $\delta_{\rm{GDR}}$ values measured in the Milky Way. In addition to possible variations of $\alpha_{\rm{CO}}$ due to the radial metallicity gradient, we test the possibility of variations in $\alpha_{\rm{CO}}$ due to changes in the underlying cloud populations, as a function of galactic radius. Using a truncated power-law molecular cloud CO luminosity function and an empirical power-law relation for cloud-mass and luminosity, we show that the changes in the underlying cloud population may account for a factor of $\sim 1.5-2.0$ radial change in $\alpha_{\rm{CO}}$.