Upper panel: mass-to-length (M/L) ratio for all filaments and for those associated with massive star forming clumps are shown as grey and red hatched histograms, respectively. The vertical cyan lines show the critical M/L thresholds for filaments with line-widths of 0.7 and 1.2 km s^-1; this corresponds to masses per unit length of 230 and 670 M_⊙ pc^-1, respectively. Filaments above these thresholds are unstable to radial collapse (see Sect. 5.5 for details). The bin size is 0.2 dex. Lower panel: the mass-to-length ratio is plotted as a function of heliocentric distance; the dashed cyan curve in this plot indicates the sensitivity of the ATLASGAL survey.