{
  "abstract": "One-dimensional self-gravitating systems admit genuine thermodynamical equilibria. For systems with strictly monotonic orbital frequency profile, the Landau and Balescu-Lenard theories predict a relaxation time scaling linearly with the number of particles, $N$, in agreement with simulations. Yet, these theories become ill-posed for degenerate frequency profiles, as is the case in the harmonic potential, where all particles share the exact same mean orbital frequency. Using an exact collision-driven 1D integrator, we investigate numerically 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 low $N$, but transition to the linear, non-degenerate behaviour for larger $N$. The larger the fraction of degenerate orbits, the larger the value of $N$ at which this transition of dynamical regime occurs. Finally, we explore the dynamics of fully non-degenerate systems, albeit with finite radial support: we confirm that their relaxation time scales linearly with $N$, though with a substantially larger prefactor than in non-compact systems. Astrophysically, this investigation should offer some new clues on the dynamics of density cores, as in the center of dwarf galaxies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2603.11238",
  "author_total": 3,
  "authors": [
    {
      "name": "Kerwann Tep"
    },
    {
      "name": "Jean-Baptiste Fouvry"
    },
    {
      "name": "Christophe Pichon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7rkkaw1pxjjf4.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "7rkkaw1pxjjf4",
  "issns": [],
  "landing_url": "https://hal.science/hal-05760118v1",
  "language": "en",
  "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": [
    [
      "hal",
      "0.phys"
    ],
    [
      "hal",
      "1.phys.astr"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05760118/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7rkkaw1pxjjf4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:39Z",
      "native_id": "hal-05760118",
      "source": "hal",
      "url": "https://hal.science/hal-05760118v1"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "hal:1.phys.astr",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "hal:0.phys",
      "subfield": "general"
    }
  ],
  "title": "Very long-term relaxation of harmonic 1D self-gravitating systems",
  "title_text": "Very long-term relaxation of harmonic 1D self-gravitating systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:39Z",
  "url": "https://research.draconitic.com/paper/7rkkaw1pxjjf4",
  "venue": "HAL",
  "versions": []
}