{
  "abstract": "In the matrix method for linear perturbations of spherical stellar systems, the perturbed potential and density are expanded over a set of potential-density pairs. For radial perturbations, mass conservation makes the coefficient of $1/r$ in the perturbed potential vanish, so that the potential decays faster than $1/r$. Starting from the $\\ell=0$ Hernquist--Ostriker family, we construct in closed form a set of potential-density pairs whose potentials decay as $r^{-p}$ with a prescribed $p\\ge2$, the tail containing all subsequent integer powers. For $p=2$ each pair is individually massless, and the potential of the $n$-th pair is expressed through a single Jacobi polynomial. We derive the combination weights, the leading tail coefficients and the Gram matrix analytically; the Gram matrix is banded with half-width $p-1$ (tridiagonal at $p=2$). The $n$-th potential element has exactly $n-1$ nodes, spread from $r\\sim n^{-2}$ to $r\\sim n^{2}$, so that the set resolves both the centre and the far periphery. As a test, the expansion of the dilation-mode potential of the isochrone model converges exponentially and carries no parasitic mass at any truncation, in contrast to the standard set.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25308",
  "author_total": 2,
  "authors": [
    {
      "name": "E. V. Polyachenko"
    },
    {
      "name": "I. G. Shukhman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/54yjzy8h09nag.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25308",
  "fulltext_url": null,
  "id": "54yjzy8h09nag",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25308",
  "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",
      "3103|Galaxies: Formation, Evolution, Phenomena"
    ]
  ],
  "openalex": "W7214082281",
  "pdf_url": "https://arxiv.org/pdf/2609.25308",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/54yjzy8h09nag.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.25308",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25308"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.GA",
      "subfield": "galaxies"
    }
  ],
  "title": "A radial basis of massless potential-density pairs",
  "title_text": "A radial basis of massless potential-density pairs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:39Z",
  "url": "https://research.draconitic.com/paper/54yjzy8h09nag",
  "venue": "arXiv",
  "versions": []
}