Beam convolution effect for model filaments with Plummer-like radial profiles (see Eq. (1)). (a) Intrinsic Plummer profile with p = 2 on top of a uniform background (solid curve), compared to a Gaussian beam on top of the same background (dash-dotted curve, here assuming ), and to the model profile after convolution with the beam (dashed curve). (b) Measured HP diameter (D_HP or hd) against HPBW spatial resolution, both in units of the intrinsic HP diameter, , for Plummer-like filaments with logarithmic density slopes p = 1.5 (solid blue curve), p = 2 (solid red curve), and p = 2.5 (solid purple curve). The dash-dotted blue curve shows the results of Gaussian fit measurements in the case of Plummer models with p = 1.5. The horizontal dashed line shows the deconvolved HP diameter, , which coincides with in the absence of noise. In contrast, the dashed blue, red, and purple curves illustrate that naive deconvolution of Gaussian fit measurements fails to recover the intrinsic diameters of Plummer models (with p = 1.5, p = 2, and p = 2.5, respectively), even in the absence of noise. The green line marks the beam HPBW. The vertical dotted segments at the bottom mark the spatial resolutions of the Arzoumanian et al. (2019) measurements assuming pc.