{
  "abstract": "We assess a surface-density anisotropy diagnostic, $A_{\\rm ani}$, and its association with the slope $α$ of a power-law galaxy profile. We reprocess 20-annulus profiles of 85 optically rich clusters on a canonical grid, $0 \\leq A_{\\rm ani} \\leq 1.92$, and an extended grid reaching 1.99. Twenty-four canonical fits and 12 extended fits reach their respective upper boundaries; 69 of 85 upper $Δχ^2=1$ bounds remain open, and only four clusters have two-sided intervals. Among 40 preselected power-law fits, the observed $α$-$A_{\\rm ani}$ Spearman coefficient is 0.616. In a model-native forward-recovery experiment with 11 injected values, all 935 noiseless profiles recover the input within 0.02. Across 46,750 Poisson catalogs matched to observed count and background conditions, recovery instead has root-mean-square error (RMSE) 0.992 and Spearman $ρ=0.093$; 40.0% of fits reach the canonical upper boundary and 81.4% have an open upper interval. Fixing both background and radial scale improves RMSE to 0.564 in a 9,350-catalog sensitivity test. As a separate structural control, 4,250 Poisson catalogs generated from fitted power laws reproduce the observed slope association: the median mock coefficient for the 40-cluster subset is 0.608 (95% range 0.453-0.731). Thus the diagnostic is numerically recoverable under its defining model without noise, but the available photometry does not reliably identify it for individual clusters. The power-law correlation can arise from shared projected profile shape and is not independent evidence for orbital anisotropy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06941",
  "author_total": 2,
  "authors": [
    {
      "name": "Sardor Sharipbayevich Kutlimuratov"
    },
    {
      "name": "Ikram Uralbayevich Tadjibayev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/66bv958qh3f4s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06941",
  "fulltext_url": null,
  "id": "66bv958qh3f4s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06941",
  "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": "W7220974037",
  "pdf_url": "https://arxiv.org/pdf/2610.06941",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/66bv958qh3f4s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.06941",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06941"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.GA",
      "subfield": "galaxies"
    }
  ],
  "title": "Power-law Coupling and Mock Validation of a Surface-density Anisotropy Diagnostic for 85 Rich Galaxy Clusters",
  "title_text": "Power-law Coupling and Mock Validation of a Surface-density Anisotropy Diagnostic for 85 Rich Galaxy Clusters",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:22Z",
  "url": "https://research.draconitic.com/paper/66bv958qh3f4s",
  "venue": "arXiv",
  "versions": []
}