Radial gas density slopes of all target clumps. Left panel: density power-law slope derived from continuum (q) based on RADMC-3D modeling detailed in Appendix E. The luminosity, clump mass, and enclosed mass within 0.5 pc are calculated from the RADMC-3D best-fit model, as listed in Table 6. Right panel: density power-law slope derived from n(H₂) maps (q_radex) from the CH₃OH RADEX modeling detailed in Sect. 3.5. The yellow horizontal line in both plots shows a slope of –1.5, indicating the free-falling density profile of a singular isothermal sphere (with an initial density slope of –2) as in Shu 1977, and the attractor solution of the gravo-turbulent collapsing in Murray et al. (2017).