Abstract

We compare the observational properties between $^{12}$CO, $^{13}$CO, and C$^{18}$O and summarize the observational parameters based on 7069 clouds sample from the Milky Way Imaging Scroll Painting (MWISP) CO survey in a section of the third Galactic quadrant. We find that the $^{13}$CO angular area ($A_{\rm ^{13}CO}$) generally increases with that of $^{12}$CO ($A_{\rm ^{12}CO}$), and the ratio of $A_{\rm ^{13}CO}$ to $A_{\rm ^{12}CO}$ is 0.38 by linear fitting. We find that the $^{12}$CO and $^{13}$CO flux are tightly correlated as $F_{\rm ^{13}CO}~=~0.17~ F_{\rm ^{12}CO}$ with both fluxes calculated within the $^{13}$CO-bright region. This indicates that the abundance $X_{\rm ^{13}CO}$ is a constant to be 6.5$^{+0.1}_{-0.5}$ $\times 10^{-7}$ for all samples under assumption of local thermodynamic equilibrium (LTE). Additionally, we observed that the X-factor is approximately constant in large sample molecular clouds. Similarly, we find $F_{\rm C^{18}O}~=~0.11~F_{\rm ^{13}CO}$ with both fluxes calculated within C$^{18}$O-bright region, which indicates that the abundance ratios ${X_{\rm ^{13}CO}/X_{\rm C^{18}O}}$ stays the same value 9.7$^{+0.6}_{-0.8}$ across the molecular clouds under LTE assumption. The linear relationships of $F_{\rm ^{12}CO}$ vs. $F_{\rm ^{13}CO}$ and $F_{\rm ^{13}CO}$ vs. $F_{\rm C^{18}O}$ hold not only for the $^{13}$CO-bright region or C$^{18}$O-bright region, but also for the entire molecular cloud scale with lower flux ratio. The abundance ratio ${X_{\rm ^{13}CO}/X_{\rm C^{18}O}}$ inside clouds shows a strong correlation with column density and temperature. This indicates that the ${X_{\rm ^{13}CO}/X_{\rm C^{18}O}}$ is dominated by a combination of chemical fractionation, selectively dissociation, and self-shielding effect inside clouds.