Power-law index of and T_dust profile. The whole T_dust and of the clump are taken from updated Y17 properties in this paper. The p values are derivedfrom Hi-GAL PPMAP data. Panels a and b: column density and dust temperature power-law index p, respectively.The crosses represent the typical errors. The dots with gray stars, white stars, and without stars represent the S-type AS, O-type AS, and NA HMSCs, respectively. The red, orange, and blue solid lines represent the median values for S-type AS, O-type AS, and NA, respectively. The red, orange, and blue dashed lines represent the median values for S-type AS, O-type AS, and NA in the corresponding column density or temperature bins. Sub-figures in the top right show the power-law index and its relation with distance. The red, orange, and blue dots represent S-type AS, O-type AS, and NA, respectively. The red, orange, and blue short lines show the median values in different distance bins for the corresponding types of HMSCs.