{
  "abstract": "Aims. Filamentary structures in molecular clouds are widely recognized as fundamental components of star formation. Observations report a length-mass relation of the form $L \\propto M^α$ with $α\\simeq 0.5$. 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 $\\sim 10^{21}$--$\\sim 10^{23}\\,\\mathrm{cm}^{-2}$. Across multiple resolutions and, separately, the full hierarchical decomposition at the highest resolution, the ensemble exhibits a sub-linear $L-M$ relation close to $L \\propto M^{0.5}$. When individual structures are traced across resolutions, the slopes remain sub-linear ($α\\simeq 0.45$--$0.70$), consistent with the geometric prediction $L \\propto M^{0.5}$ of a fragmentation-driven random walk. In contrast, decomposing individual structures at the highest resolution yields a wide range of slopes ($α\\simeq 0.2$--$3$), 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 $α\\simeq 0.5$ is a robust property of the hierarchical structure and fragmentation occurring in molecular clouds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19369",
  "author_total": 3,
  "authors": [
    {
      "name": "Rahul Patel"
    },
    {
      "name": "Daniel Seifried"
    },
    {
      "name": "Alvaro Hacar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f424x18w8qtdz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19369",
  "fulltext_url": null,
  "id": "f424x18w8qtdz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19369",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.GA"
    ],
    [
      "arxiv",
      "astro-ph.SR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.19369",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f424x18w8qtdz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2609.19369",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19369"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.GA",
      "subfield": "galaxies"
    },
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.SR",
      "subfield": "stellar"
    }
  ],
  "title": "Characterizing the hierarchical structure of filaments I. On the origin of the length-mass (L-M) scaling relation",
  "title_text": "Characterizing the hierarchical structure of filaments I. On the origin of the length-mass (L-M) scaling relation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:54Z",
  "url": "https://research.draconitic.com/paper/f424x18w8qtdz",
  "venue": "arXiv",
  "versions": []
}