{
  "abstract": "We use the core-radius, $r_γ,$ of a galaxy's central core along with a volume-limited sample of brightest cluster galaxies (BCG) to determine the $z=0$ mass distribution function of the most massive super-massive black holes (SMBH). We recover a $M_{BH}-r_γ$ relationship between the SMBH mass, $M_{BH},$ and $r_γ$ of form $M_{BH} \\approx1.3\\times10^{10}~(r_γ/{\\mathrm{kpc}})~M_\\odot,$ with $σ= 0.25\\pm0.03$ dex scatter in $M_{BH}.$ We derive a core distribution function (CDF), based on HST and DLS images of the BCGs. The CDF falls steeply as $N(r_γ)\\sim r_γ^{-3}$ for $r_γ>0.50$ kpc. Only $\\sim5\\%$ of BCGs have $r_γ>1$ kpc. Combining the CDF and $M_{BH} - r_γ$ relationship yields the BH mass distribution function (MDF). For $M_{BH} \\geq 7\\times10^{9}~\\mathrm{M_\\odot}$ (the mean $M_{BH}$ at $r_γ=0.50$ kpc) we derive: $\\log\\left(\\frac{dN(M_{BH})}{d{M_{BH}/10^{10} M_\\odot}}~[\\rm Mpc^{-3}]\\right)=(-3.05\\pm0.42)~\\log\\left(\\frac{M_{BH}}{10^{10}M_\\odot}\\right)~-~5.11\\ (+0.41, -0.36)$. Cores with $r_γ\\geq 0.50$ kpc are found almost exclusively in BCGs, implying that SMBHs with $M_{BH} \\geq7\\times10^{9}~\\mathrm{M_\\odot}$ may also be exclusive to BCGs. Core-radius correlates with $α,$ a parameter that characterizes the growth of BCG envelopes by mergers, suggesting that the most massive SMBHs grew in tandem with their BCG hosts. The BH MDF embodies a significant population of SMBH with $M_{BH} >7\\times10^{9} M_\\odot.$ When combined with the Liepold & Ma (2024) BH MDF to account for SMBH with $M_{BH} < 7\\times10^{9} M_\\odot,$ it can comfortably explain the nHz gravitational wave background.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33162",
  "author_total": 4,
  "authors": [
    {
      "name": "Marc Postman"
    },
    {
      "name": "Tod R. Lauer"
    },
    {
      "name": "Daniel J. D'Orazio"
    },
    {
      "name": "Bellamy Bailey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3n8wfmfp48ys5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33162",
  "fulltext_url": null,
  "id": "3n8wfmfp48ys5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33162",
  "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"
    ],
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "physics.space-ph"
    ],
    [
      "openalex",
      "3103|Galaxies: Formation, Evolution, Phenomena"
    ]
  ],
  "openalex": "W7223794001",
  "pdf_url": "https://arxiv.org/pdf/2610.33162",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3n8wfmfp48ys5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.33162",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33162"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.GA",
      "subfield": "galaxies"
    },
    {
      "field": "astronomy",
      "origin": "arxiv:physics.space-ph",
      "subfield": "stellar"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "The Hosts and Mass Distribution Function of the Most Massive Black Holes: Implications for the nHz Gravitational Wave Background",
  "title_text": "The Hosts and Mass Distribution Function of the Most Massive Black Holes: Implications for the nHz Gravitational Wave Background",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/3n8wfmfp48ys5",
  "venue": "arXiv",
  "versions": []
}