2022RAA....22g5006X

We revisit the mass-size relation of molecular cloud structures based on the column density map of the Cygnus-X molecular cloud complex. We extract 135 column density peaks in Cygnus-X and analyze the column density distributions around these peaks. The averaged column density profiles, N(R), around all the peaks can be well fitted with broken power-laws, which are described by an inner power-law index n, outer power-law index m, and the radius R_TP and column density N_TP at the transition point. We then explore the M-R relation with different samples of cloud structures by varying the N(R) parameters and the column density threshold, N₀, which determines the boundary of a cloud structure. We find that only when N₀ has a wide range of values, the M-R relation may largely probe the density distribution, and the fitted power-law index of the M-R relation is related to the power-law index of N(R). On the contrary, with a constant N₀, the M-R relation has no direct connection with the density distribution; in this case, the fitted power-law index of the M-R relation is equal to 2 (when N₀ >= N_TP and n has a narrow range of values), larger than 2 (when N₀ >= N_TP and n has a wide range of values), or slightly less than 2 (when N₀ < N_TP).