{
  "abstract": "The interplay of magnetic fields, turbulence, and gravity governs the structural evolution of the interstellar medium (ISM) and the initial conditions of star formation, yet observational gaps have long enforced a broken power-law description of the magnetic field--density relation. Here we assemble a unified dataset spanning ten orders of magnitude in density ($10^{-26}$--$10^{-16}\\,\\mathrm{g\\,cm^{-3}}$) by combining pulsar and Zeeman observations. The unified data are consistent with a continuous magnetic-field evolution organised by the Alfvén Mach number $\\mathcal{M}_{\\rm A}=\\sqrt{E_K/E_B}$. Within this interpretation, the low-density gas is magnetically dominated ($\\mathcal{M}_{\\rm A}<1$), whereas the high-density gas becomes kinetically dominated ($\\mathcal{M}_{\\rm A}>1$) as gravity increasingly contributes to the kinetic-energy budget, with magnetic tension continuing to influence the collapse geometry. Within the Gradual Transition interpretation, the empirical break density traces the vicinity of the trans-Alfvénic equipartition point, $\\mathcal{M}_{\\rm A}=1$. This Gradual Transition model makes three predictions tested here. Its exponent and background field are fixed in advance by turbulent physics and recovered by the fits ($β\\approx0.15$--$0.21$ against a predicted $0.147$; $B_c\\approx2.0\\,μ$G). A dense-gas fit, extrapolated blindly across four decades, passes through the diffuse pulsar data. And, under the adopted scale mappings, the implied magnetic-energy spectrum approaches a $k^{-5/3}$-like scaling on large scales and departs from this extrapolation on small scales, where gravitational compression amplifies the field. The broken power law can therefore be viewed as a piecewise approximation to the continuous magnetic equation of state, with its fitted transition density potentially retaining a physical connection to the onset of gravity-driven motions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06900",
  "author_total": 3,
  "authors": [
    {
      "name": "Mengke Zhao"
    },
    {
      "name": "Guang-Xing Li"
    },
    {
      "name": "Keping Qiu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ra26bsrxkt3h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06900",
  "fulltext_url": null,
  "id": "4ra26bsrxkt3h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06900",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.GA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.06900",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ra26bsrxkt3h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.06900",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06900"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.GA",
      "subfield": "galaxies"
    }
  ],
  "title": "A Unified Magnetohydrodynamic Scaling Relation for the Multiphase Interstellar Medium",
  "title_text": "A Unified Magnetohydrodynamic Scaling Relation for the Multiphase Interstellar Medium",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:48Z",
  "url": "https://research.draconitic.com/paper/4ra26bsrxkt3h",
  "venue": "arXiv",
  "versions": []
}