Distribution of molecular (grey dots) and atomic (HI) filaments (grey triangles) in the M–L phase space. Most data are taken from all the public surveys included in Hacar et al. (2023) (and references therein) plus some additional values from Socci et al. (2024a). Superposed to our data, we also display the M-L distribution of ATLASGAL clumps (Urquhart et al. 2018, light blue diamonds; with L = 2 × R_AGAL in our notation) and their corresponding power-law fit (dashed black line). HFS are also highlighted in this plot (blue crosses; Table A.1). Overall, most filaments follow a M-L scaling relation such as L ∝ M^0.5 (dotted blue line). We indicate the virial line mass m_vir for equipartition reported for filaments which separates the subvirial and supervirial regimes (solid red line; Eq. (5)) as well as lines of constant line mass m = [10, 100, 10³] M_⊙ pc⁻¹ (dotted grey lines). We also include the mass threshold for high-mass star formation M_HM = 870 M_⊙ ⋅ (R_eff /pc)^1.33 (dotted purple line; Kauffmann & Pillai 2010), for which we assumed L = 2 × R_eff.