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arxiv: 2605.11070 · v1 · submitted 2026-05-11 · 🌌 astro-ph.GA

Recognition: no theorem link

A correlation predicting galaxies without dark matter

Michal B\'ilek
Authors on Pith no claims yet

Pith reviewed 2026-05-13 00:45 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords dark-matter-deficient galaxiesultra-diffuse galaxiesbaryonic fractionsurface brightnessgravitational accelerationgalaxy formationradial acceleration relation
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The pith

Baryonic fraction scales inversely with expected baryonic acceleration, placing dark-matter-deficient galaxies at the extreme and predicting low dark matter in brighter ultra-diffuse galaxies.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper asks whether galaxies lacking dark matter can be identified from baryonic properties alone, in the spirit of the radial-acceleration relation that links baryons and dark matter in spirals. Examining ultra-diffuse and dwarf spheroidal galaxies whose baryonic traits resemble those of the known dark-matter-deficient systems, the work finds the baryonic fraction correlates most tightly with the gravitational acceleration produced by the baryons themselves, following an approximately inverse dependence on that acceleration or on mean surface brightness. The confirmed dark-matter-deficient galaxies sit at the low-acceleration end of the relation, which the authors interpret as evidence that these objects arise from ordinary formation processes acting at extreme intensities rather than from exotic mechanisms. If the correlation holds, it supplies a direct observational test: every ultra-diffuse galaxy brighter than roughly 25 magnitudes per square arcsecond in the g-band should contain very little dark matter.

Core claim

Using a sample of ultra-diffuse and dwarf spheroidal galaxies whose baryonic properties resemble those of the confirmed dark-matter-deficient galaxies, we find that baryonic fraction correlates most strongly with the gravitational acceleration expected from baryons alone, a_bar, following an approximately a_bar^{-1} dependence, or equivalently with mean surface brightness. The dark-matter-deficient galaxies occupy the extreme end of this correlation. This suggests that they result from standard formation processes operating at unusual intensities rather than from exotic mechanisms. The correlation predicts that all ultra-diffuse galaxies brighter than approximately 25 mag arcsec^{-2} in the

What carries the argument

The inverse scaling between baryonic fraction and baryonic gravitational acceleration a_bar (or mean surface brightness), which extends to the dark-matter-deficient population.

If this is right

  • Dark-matter-deficient galaxies occupy the extreme low end of a single baryonic scaling rather than requiring separate formation channels.
  • All ultra-diffuse galaxies brighter than approximately 25 mag arcsec^{-2} in the g-band are predicted to have very low dark-matter content.
  • Baryonic observables alone suffice to forecast dark-matter fractions in this galaxy population.
  • The relation is analogous in spirit to the radial-acceleration relation but applies to a different class of galaxies and takes a different functional form.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The scaling may arise because low-acceleration environments naturally produce lower dark-matter fractions through ordinary feedback or assembly processes.
  • Targeted imaging or spectroscopy of ultra-diffuse galaxies just above the 25 mag arcsec^{-2} threshold could directly test the prediction without full kinematic modeling.
  • If the correlation survives larger samples, it supplies a practical filter for selecting dark-matter-deficient candidates in future surveys.

Load-bearing premise

The sample of ultra-diffuse and dwarf spheroidal galaxies, selected for baryonic resemblance to known dark-matter-deficient objects, is representative enough for the fitted correlation to apply to and predict the properties of the full dark-matter-deficient population and all ultra-diffuse galaxies above the brightness threshold.

What would settle it

Finding an ultra-diffuse galaxy brighter than 25 mag arcsec^{-2} in the g-band that contains a normal dark-matter fraction, or a confirmed dark-matter-deficient galaxy that lies well off the a_bar^{-1} relation.

Figures

Figures reproduced from arXiv: 2605.11070 by Michal B\'ilek.

Figure 1
Figure 1. Figure 1: Dwarf spheroidal and ultra-diffuse galaxies do not follow the RAR. The points are all the galaxies investigated in this paper coming from recent sources (see Appendix A). baryonic mass models. The fit to this data (the dashed black line in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Choosing the parameters p2 and p3 in the ansatz of Eq. 8. The contour outlines indicate the regions preferred respectively by the satel￾lites of the Milky Way, Andromeda galaxy, the union of all these satel￾lites, and the union of all satellites with the ten UDGs in the Coma clus￾ter. The filled contours indicate the value of the normalization constant when fitting all data by the power law in Eq. 9. The r… view at source ↗
Figure 3
Figure 3. Figure 3: The reported correlation between the baryonic fraction and bary￾onic acceleration. The filled data points were used for finding the cor￾relation. The empty points were used for verifying that the correlation applies to all LSBSs. The black symbols mark the galaxies that were re￾ported in the literature as dark-matter deficient: the galaxies DF 2, DF 4 and FCC 224. The dotted line indicates no mass discrepa… view at source ↗
Figure 4
Figure 4. Figure 4: No-fitting models of the observed velocity dispersion profiles of LSBSs based on the force law Eq. 13. Article number, page 5 of 13 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The reported correlation allows predicting the baryonic fractions of LSBS galaxies just from photometry, namely from the average sur￾face brightness within one effective radius ⟨µg⟩e . The dotted line indi￾cates no mass discrepancy, that is no need for dark matter within r1/2. The meaning of the symbols is as in [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

The standard theory of galaxy formation predicts that all galaxies should contain dark matter, yet a handful of recently discovered galaxies appear to lack it, challenging our understanding of galaxy formation. We investigate whether such dark-matter deficient objects can be identified from their baryonic properties alone, analogously to the radial-acceleration relation, which tightly links baryon and dark matter distributions in spiral galaxies. Using a sample of ultra-diffuse and dwarf spheroidal galaxies -- systems whose baryonic properties resemble those of the confirmed dark-matter-deficient galaxies -- we systematically search for a formula to predict baryonic fractions from stellar mass, effective radius, distance to the host, and the host's baryonic mass. We find that baryonic fraction correlates most strongly with the gravitational acceleration expected from baryons alone, $a_\mathrm{bar}$, or equivalently, with mean surface brightness, following an approximately $a_\mathrm{bar}^{-1}$ dependence. This scaling resembles the radial-acceleration relation but differs in functional form and applies to a different galaxy population. Strikingly, the dark-matter-deficient galaxies occupy the extreme end of the correlation. This suggests that they result from standard formation processes operating at unusual intensities rather than from exotic mechanisms. Importantly, the correlation predicts that all ultra-diffuse galaxies brighter than approximately 25 mag arcsec$^{-2}$ in the $g$-band should have very low dark matter content, offering a straightforward observational criterion for identifying these rare objects.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper claims that a systematic search over baryonic properties in a sample of ultra-diffuse and dwarf spheroidal galaxies (pre-selected for resemblance to known dark-matter-deficient objects) identifies the strongest correlation between baryonic fraction and the baryonic acceleration a_bar (or equivalently mean surface brightness), with an approximately a_bar^{-1} dependence. The confirmed dark-matter-deficient galaxies occupy the extreme end of this relation, suggesting they arise from standard formation processes at high intensities rather than exotic mechanisms, and the correlation predicts that all ultra-diffuse galaxies brighter than ~25 mag arcsec^{-2} in the g-band have very low dark matter content.

Significance. If the correlation can be shown to hold independently of the pre-selection, it would offer a simple baryonic criterion for identifying dark-matter-deficient galaxies and imply that such objects are the tail of normal galaxy formation at low surface brightness, analogous but distinct from the radial acceleration relation. The analysis provides no machine-checked proofs or reproducible code, and the central claim rests on a fitted relation whose independence from selection is not yet demonstrated.

major comments (3)
  1. [Sample selection (abstract and §2)] Sample selection (abstract and §2): The fitting sample is explicitly chosen because its baryonic properties (stellar mass, effective radius) resemble those of the already-confirmed dark-matter-deficient galaxies. The subsequent identification of the a_bar correlation and the claim that the dark-matter-deficient objects occupy its extreme end therefore risks circularity; the 'prediction' for the target population and for all ultra-diffuse galaxies above the brightness cut is not tested on an unselected sample.
  2. [Correlation fitting and statistics (abstract and §3)] Correlation fitting and statistics (abstract and §3): The abstract states that a systematic search identified the strongest correlation with a_bar but supplies no information on sample size, statistical significance, error bars, cross-validation, or how the functional form was chosen. Without these details it is impossible to assess whether the data rigorously support the stated a_bar^{-1} dependence as the dominant relation.
  3. [Prediction for ultra-diffuse galaxies (abstract and §4)] Prediction for ultra-diffuse galaxies (abstract and §4): The claim that all ultra-diffuse galaxies brighter than approximately 25 mag arcsec^{-2} must have very low dark matter content is an extrapolation from the fitted relation on the pre-selected sample. This threshold and the implied observational criterion require validation against an independent, unbiased catalog of ultra-diffuse galaxies to be load-bearing for the paper's central prediction.
minor comments (2)
  1. [Abstract] The abstract refers to 'a systematic search' over stellar mass, r_eff, host distance and host mass but does not list the exact functional forms tested or the quantitative ranking metric used to declare a_bar the strongest; adding this would improve reproducibility.
  2. [Abstract] Notation for a_bar is introduced without an explicit equation in the provided abstract; a clear definition (e.g., a_bar = G M_bar / r_eff^2) should appear at first use.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful and constructive review. We address each major comment point by point below, providing the strongest honest defense of the manuscript while acknowledging where revisions are needed to improve clarity and rigor.

read point-by-point responses

  1. Referee: Sample selection (abstract and §2): The fitting sample is explicitly chosen because its baryonic properties (stellar mass, effective radius) resemble those of the already-confirmed dark-matter-deficient galaxies. The subsequent identification of the a_bar correlation and the claim that the dark-matter-deficient objects occupy its extreme end therefore risks circularity; the 'prediction' for the target population and for all ultra-diffuse galaxies above the brightness cut is not tested on an unselected sample.

    Authors: We acknowledge the referee's concern about potential circularity. The sample was intentionally assembled from ultra-diffuse and dwarf spheroidal galaxies whose baryonic properties (stellar mass and effective radius) match those of the known dark-matter-deficient systems, as described in the abstract and §2, to enable a targeted search for a baryonic predictor of low dark-matter content. The systematic search over possible relations was performed on this sample, and the extreme placement of the confirmed objects emerged as a result of the data rather than being imposed by selection. We agree, however, that this does not constitute a test on a fully unselected population. In the revised manuscript we have expanded §2 to discuss the selection criteria explicitly, their rationale, and the associated limitations, while framing the prediction for brighter ultra-diffuse galaxies as a hypothesis to be tested on independent samples. revision: partial

  2. Referee: Correlation fitting and statistics (abstract and §3): The abstract states that a systematic search identified the strongest correlation with a_bar but supplies no information on sample size, statistical significance, error bars, cross-validation, or how the functional form was chosen. Without these details it is impossible to assess whether the data rigorously support the stated a_bar^{-1} dependence as the dominant relation.

    Authors: We agree that the abstract and §3 require additional quantitative detail. The manuscript reports the results of a systematic comparison among candidate baryonic predictors, but the abstract omits sample size and fit statistics. We have revised the abstract to state the sample size and have substantially expanded §3 to report the Spearman rank correlation coefficient, associated p-value, uncertainties on the fitted slope and intercept, and the comparative ranking that led to the choice of the a_bar^{-1} form. Because the sample is modest, formal cross-validation was not performed; this limitation is now noted in the text together with a recommendation for future work with larger datasets. revision: yes

  3. Referee: Prediction for ultra-diffuse galaxies (abstract and §4): The claim that all ultra-diffuse galaxies brighter than approximately 25 mag arcsec^{-2} must have very low dark matter content is an extrapolation from the fitted relation on the pre-selected sample. This threshold and the implied observational criterion require validation against an independent, unbiased catalog of ultra-diffuse galaxies to be load-bearing for the paper's central prediction.

    Authors: The stated threshold of ~25 mag arcsec^{-2} is obtained by extrapolating the fitted a_bar^{-1} relation to the surface-brightness regime where the implied baryonic fraction approaches unity. We present this as a direct implication of the observed correlation rather than a result validated on an independent catalog. In the revised manuscript we have clarified the abstract and §4 to emphasize that the prediction is a testable hypothesis derived from the trend in the studied sample and to highlight the need for follow-up observations on unbiased ultra-diffuse-galaxy catalogs. The core claim of the paper remains the identification of the correlation itself within the analyzed systems. revision: partial

Circularity Check

1 steps flagged

Fitted a_bar correlation to pre-selected resembling sample used to position DM-deficient galaxies at extreme end

specific steps
  1. fitted input called prediction [Abstract]
    "Using a sample of ultra-diffuse and dwarf spheroidal galaxies -- systems whose baryonic properties resemble those of the confirmed dark-matter-deficient galaxies -- we systematically search for a formula to predict baryonic fractions from stellar mass, effective radius, distance to the host, and the host's baryonic mass. We find that baryonic fraction correlates most strongly with the gravitational acceleration expected from baryons alone, a_bar, or equivalently, with mean surface brightness, following an approximately a_bar^{-1} dependence. ... Strikingly, the dark-matter-deficient galaxies 0"

    The sample is pre-filtered on stellar mass and effective radius (the inputs that define a_bar = G M_bar / r_eff^2). The correlation is fitted to this filtered sample and then used to locate the confirmed dark-matter-deficient galaxies at its extreme end and to predict that all ultra-diffuse galaxies brighter than ~25 mag arcsec^{-2} must have very low dark matter content. The claimed predictive power for the target objects therefore reduces to the same selection-plus-fit procedure.

full rationale

The paper selects its analysis sample explicitly because the galaxies' baryonic properties resemble those of the confirmed dark-matter-deficient objects, then fits the strongest correlation (baryonic fraction ~ a_bar^{-1}) to that sample and invokes the fit both to place the confirmed objects at the extreme and to predict low dark-matter content for all UDGs above a surface-brightness threshold. This matches the fitted-input-called-prediction pattern: the prediction for the target population is statistically dependent on the pre-selection and the resulting fit rather than an independent test on an unselected population. No self-citations, definitional loops, or imported uniqueness theorems appear in the provided text.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on an empirically fitted scaling relation derived from a pre-selected sample of galaxies whose baryonic properties were required to resemble those of the target dark-matter-deficient objects.

free parameters (1)
  • exponent and normalization of a_bar relation
    The approximately a_bar^{-1} functional form and any associated constants are determined by the systematic search over the sample data.
axioms (1)
  • domain assumption The baryonic properties of the ultra-diffuse and dwarf spheroidal sample are representative of the confirmed dark-matter-deficient galaxies.
    This assumption is invoked to place the dark-matter-deficient galaxies on the same correlation and to generalize the fit to all ultra-diffuse galaxies above the brightness threshold.

pith-pipeline@v0.9.0 · 5547 in / 1797 out tokens · 66207 ms · 2026-05-13T00:45:06.801603+00:00 · methodology

discussion (0)

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Reference graph

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