Total velocity dispersion versus observed central column density (uncorrected for inclination effects): blue for IC 5146, magenta for Aquila, cyan for Polaris, red for NGC 2264C, and green for DR21 filaments. The squares and triangles correspond to velocity dispersions measured from N₂H ⁺  spectra and C¹⁸O spectra, respectively. See text for details on the error bars and for uncertainties in the column densities. The horizontal dashed line shows the value of the sound speed  ~ 0.2 km s^-1 for T = 10 K. The vertical dashed line marks the boundary between thermally subcritical and thermally supercritical filaments where the estimated mass per unit length M_line is approximately equal to the critical value M_line,crit ~ 16   M_⊙/pc for T = 10 K, equivalent to a column density of 8 × 10²¹ cm^-2. The grey band shows a dispersion of a factor of 3 around this nominal value. The dotted line running from the bottom left to the top right corresponds to σ_tot ∝ N_H2^0.5 normalized to 0.2 km s^-1 at the subcritical/supercritical boundary. The blue solid line shows the best power-law fit σ_tot ∝ N_H2^{0.35    ±    0.14} to the supercritical filaments.