We present a systematic analysis of scale-dependent properties of filamentary structures in seven nearby molecular clouds --, , , , , , and -- using the multiscale extraction method. Alongside the usual surface density profiles Σ (r), we derived volume density profiles ̊ho (r) for a large sample of filaments, providing new observational constraints on their three-dimensional structure. The half-maximum widths H and h of the surface and volume density profiles, respectively, systematically increase with the spatial scale, following power laws tilde Taurus Ophiuchus Perseus Orion A California IC 5146 Vela C getsf H ∝ Y^ 0. 50 and tilde h ∝ Y^ 0. 37, with distributions spanning ∼, 0. 01--1, pc across all scales, challenging the notion of a universal filament width of ∼, 0. 1, pc. The median volume density slopes tildeβ ≈ 2. 1--2. 4 are systematically lower than the value β = 4 expected for an isothermal cylinder in hydrostatic equilibrium. For shallow profiles with β łesssim 1, the volume density width h falls below the surface density width H by one to two orders of magnitude, demonstrating that surface density widths overestimate the true physical extent of filaments with shallow profiles. Volume density contrasts are substantially higher than surface density contrasts C _ ̊ho ≈ 17--52 versus tilde C _Σ ≈ 1. 1--2. 7), confirming that filaments are substantially more prominent in three dimensions than their projected appearance suggests. The median linear densities of filaments increase linearly with the spatial scale, tildeΛ ∝ Y, with the fraction of supercritical filaments (Λ > 15, M_⊙, pc-1) increasing strongly with the scale and varying widely among clouds, from ∼, 7% in Taurus and Ophiuchus to ∼, 54% in Vela C, which is broadly consistent with the known star formation activity of the clouds. The statistical properties of the combined filament linear density function across all seven clouds will be presented in a subsequent paper. Measured filament widths and slopes systematically depend on the angular resolution and distance, highlighting the importance of accounting for resolution bias in comparative filament studies.
Zhang et al. (Wed,) studied this question.