Characterizing the hierarchical structure of filaments I. On the origin of the length-mass (L-M) scaling relation

@misc{patel2026characterizing,
  title = {{Characterizing the hierarchical structure of filaments I. On the origin of the length-mass (L-M) scaling relation}},
  author = {Rahul Patel and Daniel Seifried and Alvaro Hacar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.19369},
  eprint = {2609.19369},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19369},
}

TY  - UNPB
TI  - Characterizing the hierarchical structure of filaments I. On the origin of the length-mass (L-M) scaling relation
AU  - Rahul Patel
AU  - Daniel Seifried
AU  - Alvaro Hacar
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.19369
UR  - https://arxiv.org/abs/2609.19369
AB  - Aims. Filamentary structures in molecular clouds are widely recognized as fundamental components of star formation. Observations report a length-mass relation of the form L ∝ M^α with α≃ 0.5. We characterize this relation in simulated molecular clouds and investigate the influence of hierarchical fragmentation and spatial resolution. Methods. We apply a two-step filament identification method to high-resolution 3D hydrodynamical and magnetohydrodynamical simulations from the SILCC-Zoom project, combining the Rolling Hough Transform with dendrogram-based segmentation for hierarchical decomposition. We analyze the resulting structures across multiple spatial resolutions. Results. The identified structures span column densities of ∼ 10^21--∼ 10^23 cm^−2. Across multiple resolutions and, separately, the full hierarchical decomposition at the highest resolution, the ensemble exhibits a sub-linear L−M relation close to L ∝ M^0.5. When individual structures are traced across resolutions, the slopes remain sub-linear (α≃ 0.45--$0.70$), consistent with the geometric prediction L ∝ M^0.5 of a fragmentation-driven random walk. In contrast, decomposing individual structures at the highest resolution yields a wide range of slopes (α≃ 0.2--$3$), peaking at α<1. A simple toy model shows that this diversity arises from differences in the internal column-density distribution and segmentation geometry. Conclusions. Taken together, these results indicate that the average sub-linear length-mass relation with α≃ 0.5 is a robust property of the hierarchical structure and fragmentation occurring in molecular clouds.
ER  -