Mean apparent HP width vs. spatial resolution for both HGBS filaments (red squares from Arzoumanian et al. 2019) and Hi-GAL filaments (black circles; Schisano et al. 2014). The vertical error bars correspond to ± the standard deviations of measured widths in each HGBS cloud or Hi-GAL resolution bin. The horizontal error bars represent the Hi-GAL bin widths, which exceed the resolution uncertainties arising from the typical distance uncertainties. The blue curve shows the results of the convergence test performed on the Taurus filament in Sect. 2 (see the blue diamonds in Fig. 1). The pink curves show the theoretical expectations for Plummer-like filaments with a logarithmic density slope p = 1.7 (consistent with the slope of the Taurus filament) and intrinsic HP widths of 0.1 pc and 0.08 pc, respectively (see Sect. 3 and Fig. 2). In the 0.1 pc case, the variations in expected HP width induced by variations in the p index between 1.5 and 2.5 are displayed with yellow shading. Green lines mark 1 × beam, 1.3 × beam, 1.9 × beam, and 4 × beam.