The CO-to-H${}_2$ Conversion Factor of Galactic Giant Molecular Clouds using CO isotopologues: High-resolution $X_{\mathrm{C}\mathrm{O}}$ 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 ($\sim 20\mathrm{"}$) distribution maps of the $X_{\mathrm{C}\mathrm{O}}$ factor ($X_{\mathrm{C}\mathrm{O},\mathrm{i}\mathrm{s}\mathrm{o}}$) in individual GMCs using correlation diagrams of the CO isotopologues. It is shown that $X_{\mathrm{C}\mathrm{O},\mathrm{i}\mathrm{s}\mathrm{o}}$ is variable in each GMC within the range of $X_{\mathrm{C}\mathrm{O},\mathrm{i}\mathrm{s}\mathrm{o}}\sim (0.9-5)\times {10}^{20}$ 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 $X_{\mathrm{C}\mathrm{O},\mathrm{i}\mathrm{s}\mathrm{o}}=(2.17\pm 0.27)\times {10}^{20}$ cm${}^{-2}$ (K km s${}^{-1}{)}^{-1}$, which is consistent with that from previous studies in the Milky Way.