{
  "abstract": "The core-cusp problem is a discrepancy between simulations and observations of the slopes of inner dark matter density profiles. Splitting dwarf spheroidals by metallicity is a standard method to break the mass-anisotropy degeneracy. Four dynamical methods are applied to the 1339-star Tolstoy et al. (2023) VLT/FLAMES Sculptor catalog: spherical Jeans, GravSphere, the Walker and Peñarrubia (2011) two-population estimator, and a continuous $f(\\boldsymbol{J},[\\text{Fe}/\\text{H}])$ action-based distribution function. This work finds $Γ=2.49^{+0.23}_{-0.20}$, with 99.6\\% of the posterior lying above $Γ=2$ (84.4\\% after $λ$ calibration), robust to membership cuts and metal-poor contamination; GravSphere gives $γ=0.46^{+0.40}_{-0.28}$. Controlled mocks that hold tracer geometry fixed while breaking the metallicity-kinematics link attribute $\\sim77$--$83\\%$ of the recovered bias to geometry rather than decomposition itself. The continuous distribution function encodes a metallicity--action coupling $k_J$ inaccessible to any split-based method; a direct action-space computation on 575 stars with Gaia proper motions finds $[\\text{Fe}/\\text{H}]$ declining by $\\sim0.3\\,\\text{dex}$ across three decades in radial action. On the central-density diagnostic of Read et al. (2019), the same posteriors give $ρ_\\text{DM}(150\\,\\mathrm{pc})=1.77\\times10^8\\,M_\\odot\\,\\mathrm{kpc^{-3}}$, agreeing with their independent Sculptor measurement at $0.74σ$ and placing Sculptor in their cusp-like class. The shallow $γ$ of this work is an asymptotic quantity; the local slope at $150\\,\\mathrm{pc}$ is consistent with the Navarro--Frenk--White profile under the spherical models used here, though a recent axisymmetric analysis using resolved 3D velocities finds a shallow slope over that range and identifies an inclination degeneracy to which spherical models are blind.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.23618",
  "author_total": 1,
  "authors": [
    {
      "name": "Rishi Sanjeev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1jw7cxqbgntxc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.23618",
  "fulltext_url": null,
  "id": "1jw7cxqbgntxc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.23618",
  "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": "W7204247290",
  "pdf_url": "https://arxiv.org/pdf/2608.23618",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1jw7cxqbgntxc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2608.23618",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.23618"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.GA",
      "subfield": "galaxies"
    }
  ],
  "title": "Constraining the Inner Dark-Matter Slope of Sculptor: A Comparative Analysis of Dynamical Methods",
  "title_text": "Constraining the Inner Dark-Matter Slope of Sculptor: A Comparative Analysis of Dynamical Methods",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:16Z",
  "url": "https://research.draconitic.com/paper/1jw7cxqbgntxc",
  "venue": "arXiv",
  "versions": []
}