{
  "abstract": "The effective half-light radius $R_e$ marks an arbitrary 50-per-cent light boundary, and scaling relations involving such `effective' radii and their associated surface brightnesses, $μ_e$, systematically (and undesirably) vary as the percentage changes. Here, the projected radius $R_5\\equiv R_{-2}$, where the logarithmic slope of the surface-brightness and intensity profile equals 5 mag/dex and -2, respectively, and where the luminosity per logarithmic radial interval is maximal, is developed as an alternative. It can be measured non-parametrically or with a parametrized fit. For the Sérsic $R^{1/n}$ family, $R_5=(2n/b_n)^nR_e$, with $R_5/R_e$->e$^{1/6}\\approx$1.181 as n->$\\infty$. Reparameterizing the (now $b_n$-free) $R^{1/n}$ model in terms of $R_5$ and $μ_5$ removes the non-linear $R_e$-n coupling, and because the local slope is 5 mag/dex at $R_5$, correlated measurement errors in $R_5$ and $μ_5$ better cancel when deriving the inferred total magnitude ($\\proptoμ_5-5\\log R_5$). Additionally, an exact single-integral identity is provided to relate any projected light percentage to the percentage within a sphere of the same radius. The scale radius $R_5$ is shown to be connected, through a weakly n-dependent factor to the anisotropy-insensitive internal radius $r_{-3}$, yielding a refined n-dependent Wolf-type mass estimator $M_{-3}$ and spatial mass-to-light ratio $(M_{dyn}/L)_{-3}$. Specifically, $M_{-3}\\approx4G^{-1}<σ_{los}^2>R_{-2}\\approx4.72G^{-1}<σ_{los}^2>R_e$. Past half-light substitutions in dynamical mass estimators introduce systematic Sérsic-dependent offsets of 12-18 per~cent in enclosed mass and offsets spanning >20 per~cent in the mass-to-light ratio within $r_{-3}$. Dynamical mass estimators appropriate for (dark matter)-free stellar systems are also provided, and all relations are implemented in the companion Python package R5Tools.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.17680",
  "author_total": 1,
  "authors": [
    {
      "name": "Alister W. Graham"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9n8smdv1b9cth.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.17680",
  "fulltext_url": null,
  "id": "9n8smdv1b9cth",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.17680",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.GA"
    ],
    [
      "openalex",
      "3103|Galaxies: Formation, Evolution, Phenomena"
    ]
  ],
  "openalex": "W7203785736",
  "pdf_url": "https://arxiv.org/pdf/2608.17680",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9n8smdv1b9cth.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2608.17680",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.17680"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.GA",
      "subfield": "galaxies"
    }
  ],
  "title": "$R_{\\rm e}$, or not $R_{\\rm e}$: Developing $R_5\\equiv R_{-2}$ as a scale radius for galaxy sizes, masses, and mass-to-light ratios",
  "title_text": "R_e, or not R_e: Developing R_5≡ R_−2 as a scale radius for galaxy sizes, masses, and mass-to-light ratios",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/9n8smdv1b9cth",
  "venue": "arXiv",
  "versions": []
}