Gas Column Density Distribution of Molecular Clouds in the Third Quadrant of the Milky Way

We have obtained column density maps for an unbiased sample of 120 molecular clouds in the third quadrant of the Milky Way mid-plane (b$\le |5|^{\circ}$) within the galactic longitude range from 195$^{\circ}$ to 225$^{\circ}$, using the high sensitivity $^{12}$CO and $^{13}$CO ($J=1-0$) data from the Milky Way Imaging Scroll Painting (MWISP) project. The probability density functions of the molecular hydrogen column density of the clouds, N-PDFs, are fitted with both log-normal (LN) function and log-normal plus power-law (LN+PL) function. The molecular clouds are classified into three categories according to their shapes of N-PDFs, i.e., LN, LN+PL, and UN (unclear), respectively. About 72\% of the molecular clouds fall into the LN category, while 18\% and 10\% into the LN+PL and UN categories, respectively. A power-law scaling relation, $\sigma_s\propto N_{H_2}^{0.44}$, exists between the width of the N-PDF, $\sigma_s$, and the average column density, $N_{H_2}$, of the molecular clouds. However, $\sigma_s$ shows no correlation with the mass of the clouds. A correlation is found between the dispersion of normalized column density, $\sigma_{N/\rm <N>}$, and the sonic Mach number, $\mathcal{M}$, of molecular clouds. Overall, as predicted by numerical simulations, the N-PDFs of the molecular clouds with active star formation activity tend to have N-PDFs with power-law high-density tails.