The CO-to-H$_2$ Conversion Factor of Galactic Giant Molecular Clouds using CO isotopologues: High-resolution $X_{\rm CO}$ maps

We investigated the correlation between intensities of the $^{12}$CO and $^{13}$CO ($J=1$-0) lines toward the Galactic giant molecular clouds (GMCs) W51A, W33, N35-N36 complex, W49A, M17SW, G12.02-00.03, W43, and M16 using the FUGIN (FOREST Unbiased Galactic plane Imaging survey with the Nobeyama 45-m telescope) CO line data. All the GMCs show intensity saturation in the $^{12}$CO line when the brightness temperature of $^{13}$CO is higher than a threshold temperature of about $\sim 5$ K. We obtained high-resolution ($\sim 20"$) distribution maps of the $X_{\rm CO}$ factor ($X_{\rm CO, iso}$) in individual GMCs using correlation diagrams of the CO isotopologues. It is shown that $X_{\rm CO, iso}$ is variable in each GMC within the range of $X_{\rm CO, iso} \sim (0.9 {\rm -} 5) \times 10^{20}$ cm$^{-2}$ (K km s$^{-1})^{-1}$. Despite the variability in the GMCs, the average value among the GMCs is found to be nearly constant at $X_{\rm CO, iso} = (2.17 \pm 0.27) \times 10^{20}$ cm$^{-2}$ (K km s$^{-1})^{-1}$, which is consistent with that from previous studies in the Milky Way.