Beam convolution effect for model filaments with power-law (PL) radial profiles. (a) Example of an intrinsic PL radial profile on top of a uniform background (solid curve), compared to a Gaussian beam on top of the same background (dash-dotted curve), and to the model PL profile after convolution with the beam (dashed curve). The thin solid line marks the HP level of both the convolved PL profile and the beam. (b) Plot of the ratio FWHM_obs/HPBW ≡ A_G(p) against the logarithmic slope of the radial density profile, p, for PL filaments. The two vertical dashed lines bracket the range of PL indices for observed filaments at large radii (1.5 <  p <  2.5).