Revisiting the Mass–Size Relation of Structures in Molecular Clouds

Abstract

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, N 0, which determines the boundary of a cloud structure. We find that only when N 0 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 N 0, 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 N 0 ≥ N TP and n has a narrow range of values), larger than 2 (when N 0 ≥ N TP and n has a wide range of values), or slightly less than 2 (when N 0 < N TP).