Radial column density profiles (with background subtraction and normalized to the central column density, N(0)) of both observations (solid red curves) and polytropic cylinder models with n = −1, −2, −3, −4 (dashed curves). The radius is normalized to ϖ₀. The black crosses indicate the observation data points. The top and bottom panels describe regions R1 and R2 of the filament, respectively.