{
  "abstract": "Primordial black holes (PBHs) formed in the early universe represent a well-motivated dark matter candidate. However, their abundance in the intermediate-to-high mass range ($10^6$-$10^9\\,M_\\odot$) remains relatively less constrained. In this mass regime, the corresponding Einstein radii on the milliarcsecond scale make Very Long Baseline Interferometry (VLBI) the most direct observational probe via milli-lensing of compact radio sources. In this paper, we present predictions for the abundance of PBH dark matter ($f_{\\rm PBH}$) using the large SMILE sample of $\\sim 5000$ flat-spectrum compact radio sources. Under the optimistic observational conditions (with an angular resolution of $1.5\\,\\mathrm{mas}$, a maximum image separation of $100\\,\\mathrm{mas}$, and a maximum detectable flux ratio of $40$), assuming that no milli-lensing events are confirmed, we obtain the projected 95% upper limit of $f_{\\rm PBH}\\lesssim0.12%$ in the intermediate-to-high mass range, which would be approximately an order of magnitude tighter than previous VLBI milli-lensing limits. Broader lognormal mass functions yield correspondingly weaker projected limits. Generalising the optical depth to account for magnification bias and finite-core resolvability changes these projected limits by only about $5$%. Moreover, we show that the predicted limits are highly sensitive to a small number of confirmed events, i.e., even one confirmed milli-lensing event would relax the projected upper limit to $0.20$%, highlighting the critical importance of robust candidate confirmation in the SMILE sample. Finally, under the optimistic baryonic accretion scenario, the PBH mass growth changes the projected limits by $\\lesssim 1$% within the VLBI-sensitive mass range, confirming the robustness of our results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20329",
  "author_total": 7,
  "authors": [
    {
      "name": "Xinyue Jiang"
    },
    {
      "name": "Shuo Cao"
    },
    {
      "name": "Marek Biesiada"
    },
    {
      "name": "Xuanni Chen"
    },
    {
      "name": "Yalong Nan"
    },
    {
      "name": "Xinyang Jin"
    },
    {
      "name": "Xuchen Tai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/861g3zejd68j4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20329",
  "fulltext_url": null,
  "id": "861g3zejd68j4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20329",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.20329",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/861g3zejd68j4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.20329",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20329"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    }
  ],
  "title": "Predictions on the abundance of primordial black holes: results from the SMILE VLBI milli-lensing sample",
  "title_text": "Predictions on the abundance of primordial black holes: results from the SMILE VLBI milli-lensing sample",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/861g3zejd68j4",
  "venue": "arXiv",
  "versions": []
}