{
  "abstract": "One-dimensional self-gravitating systems admit genuine thermodynamical equilibria. For systems with a strictly monotonic orbital frequency profile, the Landau and Balescu–Lenard theories predict a relaxation time that scales linearly with the number of particles, N , in agreement with simulations. These theories become ill-posed for degenerate frequency profiles, as is the case in the harmonic potential, where all particles have the exact same mean orbital frequency. Using an exact collision-driven 1D integrator, we numerically investigated the self-consistent relaxation of 1D harmonic self-gravitating systems. We show that harmonic systems relax on a timescale that grows quadratically with N . We show that systems that are only partially degenerate display the same quadratic scaling for high N, but transition to the linear non-degenerate behaviour for higher N . The larger the fraction of degenerate orbits, the higher the value of N at which this transition of dynamical regime occurs. Finally, we explored the dynamics of fully non-degenerate systems, but with finite radial support: we confirm that their relaxation time scales linearly with N , but with a substantially larger prefactor than in non-compact systems. Astrophysically, this investigation offers some new clues on the dynamics of density cores, as in the centre of dwarf galaxies.",
  "abstract_shown": true,
  "affiliations": [
    "Observatoire Astronomique de Strasbourg, CNRS UMR 7550",
    "Institut d’Astrophysique de Paris, CNRS and Sorbonne Université, UMR 7095",
    "Kyung Hee University, Department of Astronomy & Space Science"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Kerwann Tep",
      "orcid": "0009-0002-8012-4048"
    },
    {
      "affs": [
        1
      ],
      "name": "Jean-Baptiste Fouvry",
      "orcid": "0000-0002-0030-371X"
    },
    {
      "affs": [
        1,
        2
      ],
      "name": "Christophe Pichon",
      "orcid": "0000-0003-0695-6735"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9mn8zm8qfvye0.bib",
  "cited_by": 0,
  "doi": "10.1051/0004-6361/202659808",
  "fulltext_url": null,
  "id": "9mn8zm8qfvye0",
  "issns": [
    "0004-6361",
    "1432-0746"
  ],
  "landing_url": "https://www.aanda.org/10.1051/0004-6361/202659808",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3103|Galaxies: Formation, Evolution, Phenomena"
    ]
  ],
  "openalex": "W7135220594",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": "EDP Sciences",
  "ris": "https://research.draconitic.com/paper/9mn8zm8qfvye0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:18Z",
      "native_id": "10.1051/0004-6361/202659808",
      "source": "crossref",
      "url": "https://www.aanda.org/10.1051/0004-6361/202659808"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "openalex:3103|Galaxies: Formation, Evolution, Phenomena",
      "subfield": "galaxies"
    }
  ],
  "title": "Very long-term relaxation of harmonic 1D self-gravitating systems",
  "title_text": "Very long-term relaxation of harmonic 1D self-gravitating systems",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:18Z",
  "url": "https://research.draconitic.com/paper/9mn8zm8qfvye0",
  "venue": "Astronomy & Astrophysics",
  "versions": []
}