Characterizing the hierarchical structure of filaments. I. The origin of the length-mass (L-M) scaling relation
Year: 2026
Type: article
Abstract: Filamentary structures in molecular clouds are widely recognized as fundamental components of the star formation process. Observations report a scaling relation between the length and mass of these filamentary structures of the form L ∝ M^α with α ≃ 0.5. We aim to characterize this scaling relation in simulated molecular clouds and to investigate the influence of hierarchical fragmentation and spatial resolution on it. We applied a two-step filament identification method in high-resolution, 3D hydrodynamical and magnetohydrodynamical simulations of molecular clouds within the SILCC-Zoom project, combining the Rolling Hough Transform for filament identification with dendrogram-based segmentation for hierarchical decomposition. The resulting structures were analyzed across multiple spatial resolutions to quantify their scaling properties. The identified filamentary structures cover a wide range of column densities ( $). The ensemble of structures, spanning both multiple resolutions and, separately, the full hierarchical decomposition at the highest resolution, exhibits a sub-linear L-M relation close to L ∝ M^ to cm -2 0.5 . This indicates that this relation is an intrinsic property of hierarchically structured clouds rather than an artifact of resolution blending. When individual structures are traced across different resolutions, the power-law indices remain sub-linear (α ≃ 0.45 - 0.70), matching the geometric prediction L ∝ M^ 0.5 of a fragmentation-driven random walk. However, by decomposing individual structures at the highest resolution, we find a wide range of L-M slopes (α ≃ 0.2 to 3) peaking at $α < 1. We present a simple toy model that shows that this diversity arises from differences in the internal column density distribution and in the geometry of the segmentation. Taken together, the various results, which all show an average sub-linear power-law relation L ∝ M^α with α ≃ 0.5, indicate that this L-M relation is a robust property of the hierarchical structure and fragmentation occurring in molecular clouds.
Source: Astronomy and Astrophysics
Authors: Rahul Patel, Daniel Seifried, Alvaro Hacar
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,865
OpenAlex ID: W7213599458