{
  "abstract": "The distribution $f(e)=2e$ is commonly referred to as the `thermal eccentricity distribution' of Keplerian binaries. However, the result does not require thermal equilibrium, and its usual derivations obscure why the distribution is linear in eccentricity. We seek a simple geometrical interpretation of this result and its relation to more general eccentricity distributions. We consider bound Kepler orbits in a Euclidean space of dimension $D\\geq2$, with a phase-space distribution depending only on energy, and derive the eccentricity distribution from the Liouville measure. We obtain $f_D(e)=(D-1) e (1-e^2)^{(D-3)/2}$, so that, within this family, $D=3$ is the only case for which the distribution function is linear in $e$. This follows from the $D-1$ transverse momentum dimensions and the Kepler period degeneracy. We further show that two known generalisations -- namely a power-law weighting of the normalised angular momentum and a constant velocity anisotropy -- are, in fact, two representations of the same one-parameter family of eccentricity distributions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30259",
  "author_total": 1,
  "authors": [
    {
      "name": "Václav Pavlík"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/68krvqbgq244f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30259",
  "fulltext_url": null,
  "id": "68krvqbgq244f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30259",
  "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.EP"
    ],
    [
      "arxiv",
      "astro-ph.GA"
    ],
    [
      "arxiv",
      "astro-ph.SR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.30259",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/68krvqbgq244f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.30259",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30259"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.GA",
      "subfield": "galaxies"
    },
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.EP",
      "subfield": "planetary"
    },
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.SR",
      "subfield": "stellar"
    }
  ],
  "title": "The geometric origin of the thermal eccentricity law",
  "title_text": "The geometric origin of the thermal eccentricity law",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/68krvqbgq244f",
  "venue": "arXiv",
  "versions": []
}