Multi log-normal density structure in Cygnus-X molecular clouds: A fitting for N-PDF without power-law

We studied the H$_2$ column density probability distribution function (N-PDF) based on molecular emission lines using the Nobeyama 45-m Cygnus X CO survey data. Using the DENDROGRAM and SCIMES algorithms, we identified 124 molecular clouds in the $^{13}$CO data. From these identified molecular clouds, an N-PDF was constructed for 11 molecular clouds with an extent of more than 0.4 deg$^2$. From the fitting of the N-PDF, we found that the N-PDF could be well-fitted with one or two log-normal distributions. These fitting results provided an alternative density structure for molecular clouds from a conventional picture. We investigated the column density, dense molecular cloud cores, and radio continuum source distributions in each cloud and found that the N-PDF shape was less correlated with the star-forming activity over a whole cloud. Furthermore, we found that the log-normal N-PDF parameters obtained from the fitting showed two impressive features. First, the log-normal distribution at the low-density part had the same mean column density ($\sim$ 10$^{21.5}$ cm$^{-2}$) for almost all the molecular clouds. Second, the width of the log-normal distribution tended to decrease with an increasing mean density of the structures. These correlations suggest that the shape of the N-PDF reflects the relationship between the density and turbulent structure of the whole molecular cloud but is less affected by star-forming activities.