Molecular Gas Structures traced by $^{13}$CO Emission in the 18,190 $^{12}$CO Molecular Clouds from the MWISP Survey

After the morphological classification of the 18,190 $^{12}$CO molecular clouds, we further investigate the properties of their internal molecular gas structures traced by the $^{13}$CO($J=$ 1$-$0) line emissions. Using three different methods to extract the $^{13}$CO gas structures within each $^{12}$CO cloud, we find that $\sim$ 15$\%$ of $^{12}$CO clouds (2851) have $^{13}$CO gas structures and these $^{12}$CO clouds contribute about 93$\%$ of the total integrated flux of $^{12}$CO emission. In each of 2851 $^{12}$CO clouds with $^{13}$CO gas structures, the $^{13}$CO emission area generally does not exceed 70$\%$ of the $^{12}$CO emission area, and the $^{13}$CO integrated flux does not exceed 20$\%$ of the $^{12}$CO integrated flux. We reveal a strong correlation between the velocity-integrated intensities of $^{12}$CO lines and those of $^{13}$CO lines in both $^{12}$CO and $^{13}$CO emission regions. This indicates the H$_{2}$ column densities of molecular clouds are crucial for the $^{13}$CO lines emission. After linking the $^{13}$CO structure detection rates of the 18,190 $^{12}$CO molecular clouds to their morphologies, i.e. nonfilaments and filaments, we find that the $^{13}$CO gas structures are primarily detected in the $^{12}$CO clouds with filamentary morphologies. Moreover, these filaments tend to harbor more than one $^{13}$CO structure. That demonstrates filaments not only have larger spatial scales, but also have more molecular gas structures traced by $^{13}$CO lines, i.e. the local gas density enhancements. Our results favor the turbulent compression scenario for filament formation, in which dynamical compression of turbulent flows induces the local density enhancements. The nonfilaments tend to be in the low-pressure and quiescent turbulent environments of the diffuse interstellar medium.