{
  "abstract": "The central dark matter distribution probes the nature of dark matter and baryon physics, yet its impact on time-delay cosmography is not fully explored. We update previous analyses of the cluster-lensed quasar SDSS J1004+4112 and the supernova Refsdal in MACS J1149.5+2223 by replacing the main halo density profile from an elliptical Navarro-Frenk-White (NFW) profile to a cored elliptical NFW profile and investigating the impact of the central dark matter core on the Hubble constant $H_0$. We jointly infer $H_0$ and the dimensionless core size parameter $β=r_{\\rm c}/r_{\\rm s}$, while the Brightest Cluster Galaxy (BCG) is either tied to the scaling relation of cluster member galaxies or modeled separately, with its mass left free or assigned a Gaussian prior from the stellar mass estimate for a Chabrier or Salpeter initial mass function (IMF). For SDSS J1004+4112, constraints on both $β$ and $H_0$ strongly depend on the treatment of the BCG. A large core is implied when no prior is added to the BCG stellar mass, while a reasonable assumption on the BCG mass prefers a nearly cuspy halo with $β\\sim 10^{-3}$. For MACS J1149.5+2223, a large core of $β\\sim 0.5$ is obtained with no prior, while a modest core of $β=0.0410^{+0.0865}_{-0.0276}$ is preferred when the Salpeter IMF is assumed. The constraint on $H_0$ from MACS J1149.5+2223 is stable against the BCG treatment, supporting its robustness. For the Salpeter-prior case, we obtain $H_0=65.9^{+3.5}_{-3.4}\\mathrm{~km~s^{-1}~Mpc^{-1}}$, and different BCG assumptions change the median $H_0$ by less than $1σ$. The core size constraints are translated into the self-interacting dark matter cross section, giving a 95% upper limit of $σ/m<0.035\\,\\mathrm{cm}^{2}\\,\\mathrm{g}^{-1}$ from SDSS J1004+4112 and the 68% range of $σ/m=0.071^{+0.15}_{-0.045}\\,\\mathrm{cm}^{2}\\,\\mathrm{g}^{-1}$ from MACS J1149.5+2223.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39796",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuting Liu"
    },
    {
      "name": "Masamune Oguri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/23cnk05ypy7rv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39796",
  "fulltext_url": null,
  "id": "23cnk05ypy7rv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39796",
  "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.CO"
    ],
    [
      "openalex",
      "3103|Cosmology and Gravitation Theories"
    ]
  ],
  "openalex": "W7215035732",
  "pdf_url": "https://arxiv.org/pdf/2609.39796",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/23cnk05ypy7rv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39796",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39796"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    }
  ],
  "title": "Effects of a central dark matter core on time-delay cosmography with galaxy clusters",
  "title_text": "Effects of a central dark matter core on time-delay cosmography with galaxy clusters",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/23cnk05ypy7rv",
  "venue": "arXiv",
  "versions": []
}