FWHM-N_H(0) relation of filaments. Observed values in Polaris (dark grey symbols), IC 5146 (black symbols), and Aquila (light grey symbols), from Fig. 7 of Arzoumanian et al. (2011). Note that we are plotting the column density of H nucleons rather than H₂. We also lowered their values by 2.33/2.8 to correct for the value of that they adopted. The horizontal dashed-dotted lines give the imaging resolution achieved in the three fields (black: IC 5146, dark grey: Polaris, light grey: Aquila). Predictions from the model of pressure-confined isothermal self-gravitating cylinders are given for three different inclination angles (0°, 60°, and 80°; solid black and grey curves). The cloud temperature of the molecular gas is taken to be T = 10   K. The external pressure provided by the ambient medium is assumed to be p_ext/k = 2 × 10⁴   K   cm^-3 (see discussion in Appendix A.3). The dashed lines are the asymptotes for low and high overpressure p_c/p_ext or f_cyl (this is a logarithmic version of Fig. 8). For an overpressure corresponding to that of a critical stable sphere, and for inclination 0°, the expected value is shown as the filled black circle. Likewise, the vertical dotted line indicates the column density of a cylinder with mass ratio f_cyl = 0.75; the upper non-linear scale indicates other values of f_cyl for this inclination. The expected range for a pressure regime 1.5 to 5 × 10⁴   K   cm^-3 is shown by light grey shading.