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 RTP and column density NTP 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 ³ NTP and n has a narrow range of values), larger than 2 (when N0 ³ NTP and n has a wide range of values), or slightly less than 2 (when N0 < NTP).
methods: analytical – methods: data analysis – ISM: clouds – ISM: structure
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