The radial acceleration relation and dark baryons in MOND

Akram Hasani Zonoozi; Amir Ghari; Hosein Haghi

arxiv: 1907.01564 · v1 · pith:3SSWE6YBnew · submitted 2019-07-02 · 🌌 astro-ph.GA

The radial acceleration relation and dark baryons in MOND

Amir Ghari , Hosein Haghi , Akram Hasani Zonoozi This is my paper

Pith reviewed 2026-05-25 10:38 UTC · model grok-4.3

classification 🌌 astro-ph.GA

keywords MONDradial acceleration relationdark baryonsrotation curvesSPARC galaxiesuniversal constantsurface brightnessinterpolating function

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The pith

MOND critical acceleration a0 shows no correlation with central surface brightness, supporting it as a universal constant.

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

The paper fits the rotation curves of SPARC disk galaxies in modified Newtonian dynamics, testing both the standard interpolating function and an empirical RAR-inspired one. It includes cold dark baryons by scaling the observed atomic gas mass by a constant factor c, which yields slightly better fits for about 47 percent of the galaxies with a mean c around 2.4. This scaling also lowers the fitted characteristic acceleration g_dag by roughly 40 percent. The central result is the absence of any correlation between the MOND critical acceleration a0 and the central surface brightness of the stellar disk. A sympathetic reader would conclude that a0 behaves as the same fixed value for galaxies across a range of masses, sizes, and brightnesses.

Core claim

When the SPARC rotation curves are modeled in MOND with an optional scaling factor c applied to the atomic mass to represent cold dark baryons, the best-fit value of a0 remains uncorrelated with the central surface brightness μ3.6. This lack of correlation holds whether or not dark baryons are included, and it supports treating a0 as a universal constant rather than one that varies with galaxy properties.

What carries the argument

Scaling the atomic gas mass by a single constant factor c to include cold dark baryons in the mass budget, then fitting the radial acceleration relation with standard and RAR-inspired interpolating functions to extract a0 and g_dag.

If this is right

a0 can be applied as the same numerical value to all rotationally supported galaxies without adjustment for surface brightness
Accounting for dark baryons via the scaling reduces the required value of the characteristic acceleration g_dag
Slightly improved rotation-curve fits occur for a subset of galaxies when c exceeds 1
The radial acceleration relation remains tight even after the inclusion of the scaled dark baryons

Where Pith is reading between the lines

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

Independent maps or mass measurements of cold molecular gas could test whether the constant scaling factor c matches real distributions
If a0 is truly universal, MOND models gain a fixed scale that does not need retuning when applied to new galaxy populations
The 40 percent drop in g_dag when dark baryons are added might be checked against other acceleration scales measured in the same galaxies

Load-bearing premise

The modeling choice that cold dark baryons can be represented simply by scaling the atomic mass by a constant factor c without independent observational constraints on their distribution or amount.

What would settle it

A statistically significant correlation between the best-fit a0 and central surface brightness μ3.6 appearing in a larger or morphologically different galaxy sample would falsify the claim that a0 is universal.

read the original abstract

Recent observations of rotationally supported galaxies show a tight correlation between the observed radial acceleration at every radius and the Newtonian acceleration generated by the baryonic mass distribution, the so-called radial acceleration relation (RAR). The rotation curves (RCs) of the SPARC sample of disk galaxies with different morphologies, masses, sizes and gas fractions are investigated in the context of modified Newtonian dynamics (MOND). We include the effect of cold dark baryons by scaling the measured mass in the atomic form by a factor of $c$ in the mass budget of galaxies. In addition to the standard interpolating function, we also fit the RCs and the RAR with the empirical RAR-inspired interpolating function. Slightly better fits for about $47\%$ of galaxies in our sample are achieved in the presence of dark baryons ($c>1$) with the mean value of $c = 2.4\pm 1.3$. Although the MOND fits are not significantly improved by including dark baryons, it results in a decrease in the characteristic acceleration $g_\dag$ by $40\%$. We find no correlation between the MOND critical acceleration $a_0$ and the central surface brightness of the stellar disk, $\mu_{3.6}$. This supports $a_0$ being a universal constant for all galaxies.

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.

Desk Editor's Note private letter to a colleague

The paper reports that a fitted scaling c on atomic gas improves some MOND fits to SPARC and drops g_dag by 40%, with no a0-mu_3.6 correlation, but the unconstrained c risks shifting the per-galaxy a0 values used for that claim.

read the letter

The core result is that allowing a constant c to boost the atomic gas mass for cold dark baryons yields slightly better MOND rotation-curve fits for 47% of the SPARC sample, with mean c = 2.4, and lowers the characteristic acceleration g_dag by 40%. They also report no correlation between the fitted a0 and central stellar surface brightness, which they take as support for a0 being universal. The work applies both the standard interpolating function and the RAR-inspired one to the same data set after the scaling is introduced. That quantitative outcome on c and the shift in g_dag is the concrete addition relative to prior MOND analyses of SPARC. The modeling is straightforward and the sample is the usual one, so the numbers are easy to compare with earlier papers. The main limitation is that c is determined by fitting the same rotation curves that are then used to extract a0; there is no external constraint on the amount or radial distribution of the extra mass. Because g_N changes directly with c, any mismatch between the assumed scaling and the true distribution will move the best-fit a0 for individual galaxies, which could suppress or induce a correlation with mu_3.6. The abstract gives no error bars on the correlation coefficient or details on how the fits were performed, so the strength of the no-correlation statement is hard to judge from what is shown. This is a narrow extension aimed at people already working on MOND versus dark-matter explanations for the RAR. It does not introduce new theory or independent data, but the SPARC re-analysis with the extra parameter is worth checking in detail. I would send it to referees because the question about a0 universality is worth a careful look even if the dark-baryon modeling needs tightening.

Referee Report

3 major / 2 minor

Summary. The paper analyzes the SPARC sample of disk galaxies in the MOND framework, incorporating cold dark baryons by scaling the atomic gas mass by a constant factor c in the baryonic mass budget. Rotation curves and the radial acceleration relation are fit using both the standard interpolating function and an RAR-inspired one. For ~47% of the sample, c>1 yields slightly better fits with mean c=2.4±1.3; this reduces the characteristic acceleration g_dag by 40% but does not significantly improve overall fits. The central result is the absence of correlation between the fitted MOND acceleration a0 and central surface brightness μ3.6, taken as evidence that a0 is a universal constant.

Significance. If the no-correlation result is robust, the work would strengthen MOND by showing a0 independent of galaxy surface brightness and would motivate further study of dark baryons as a possible adjustment to the baryonic mass budget. The use of both standard and empirical interpolating functions is a positive feature, as is the reporting of a mean c value.

major comments (3)

[Abstract/Methods] Abstract and methods (inferred from description of g_N computation): the scaling factor c is fitted directly to the same rotation-curve data used to determine per-galaxy a0 (or g_dag); because g_N enters the MOND relation, any mismatch between the assumed scaled atomic-gas distribution and the true dark-baryon distribution systematically shifts the best-fit a0, which is the quantity tested for correlation with μ3.6.
[Abstract] Abstract: the reported mean c=2.4±1.3 and the 40% reduction in g_dag are obtained after post-hoc fitting of c; no independent observational constraints on the amount or radial profile of the dark baryons are provided, leaving the modeling choice as an unconstrained free parameter that directly affects the central no-correlation claim.
[Results] Results (inferred): the lack of correlation between a0 and μ3.6 is presented without reported error bars on individual a0 values that propagate the uncertainty in c, or without a quantitative test (e.g., Spearman rank or partial correlation controlling for c) showing that the null result survives the additional freedom in c.

minor comments (2)

[Abstract] Notation: g_dag and a0 appear to be used interchangeably in places; clarify the distinction and which quantity is plotted against μ3.6.
[Abstract] The abstract states 'slightly better fits' for 47% of galaxies but does not specify the quantitative criterion (Δχ² threshold, AIC, etc.) used to declare improvement.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment below and indicate the revisions that will be made to strengthen the manuscript.

read point-by-point responses

Referee: [Abstract/Methods] Abstract and methods (inferred from description of g_N computation): the scaling factor c is fitted directly to the same rotation-curve data used to determine per-galaxy a0 (or g_dag); because g_N enters the MOND relation, any mismatch between the assumed scaled atomic-gas distribution and the true dark-baryon distribution systematically shifts the best-fit a0, which is the quantity tested for correlation with μ3.6.

Authors: We agree that fitting c simultaneously with a0 to the rotation-curve data can introduce a systematic shift in the inferred a0 because g_N is recomputed with the scaled gas mass. The atomic-gas radial profile is taken directly from the HI observations, so the scaling is a uniform multiplier rather than an arbitrary redistribution. Nevertheless, this remains a modeling choice that could bias a0. We will add an explicit discussion of this potential systematic effect in the revised methods and results sections and will include a comparison of the a0–μ3.6 relation obtained at fixed c = 1. revision: partial
Referee: [Abstract] Abstract: the reported mean c=2.4±1.3 and the 40% reduction in g_dag are obtained after post-hoc fitting of c; no independent observational constraints on the amount or radial profile of the dark baryons are provided, leaving the modeling choice as an unconstrained free parameter that directly affects the central no-correlation claim.

Authors: The referee correctly notes that the reported mean c and the associated shift in g_dag are obtained from fits to the same rotation-curve data and that no independent observational constraints on dark baryons are supplied. This is a genuine limitation of the present analysis. We will revise the abstract and the relevant methods paragraph to state explicitly that c is a fitted parameter without external calibration and will discuss the implications for the interpretation of the no-correlation result. revision: yes
Referee: [Results] Results (inferred): the lack of correlation between a0 and μ3.6 is presented without reported error bars on individual a0 values that propagate the uncertainty in c, or without a quantitative test (e.g., Spearman rank or partial correlation controlling for c) showing that the null result survives the additional freedom in c.

Authors: We acknowledge that the manuscript presents the a0–μ3.6 relation using best-fit a0 values without propagating the uncertainty arising from the fitted c, and without a formal statistical test that accounts for the extra degree of freedom. We will revise the results section to report a0 uncertainties that include the contribution from c and will add a quantitative correlation analysis (including a partial-correlation test controlling for c) to demonstrate that the null result is robust. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical fits yield independent result

full rationale

The paper reports fits of MOND parameters (a0 or g†) and an auxiliary scaling c to rotation-curve data, then states an empirical finding of no correlation between the resulting per-galaxy a0 values and μ3.6. The decrease in g† when c>1 is a direct numerical consequence of raising g_N, but the paper presents it as an observed outcome of the fits rather than an independent prediction. No equation reduces to another by definition, no fitted quantity is renamed as a prediction, and no load-bearing premise rests on a self-citation chain. The central claim remains a data-driven statement that could have been positive or negative correlation; the extra freedom in c affects the numerical values but does not force the reported absence of correlation by construction. The analysis is therefore self-contained against the observational sample.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The analysis relies on the MOND framework and the assumption that the SPARC sample allows for such scaling; dark baryons are postulated without external evidence. The central claim depends on fitted parameters c and g_dag.

free parameters (2)

c = 2.4 ± 1.3
Scaling factor for atomic mass to include dark baryons, fitted to improve RC fits for 47% of sample.
g_dag
Characteristic acceleration scale, reduced by 40% when including dark baryons scaling.

axioms (2)

domain assumption Validity of MOND framework and interpolating functions to explain RAR
The paper assumes MOND applies to the SPARC galaxies' dynamics.
domain assumption SPARC sample is representative of disk galaxies without major selection biases
Used as the basis for all fits and correlations in the abstract.

invented entities (1)

cold dark baryons no independent evidence
purpose: To account for unseen baryonic mass by scaling atomic mass with factor c
Postulated to improve MOND fits, with no independent evidence provided in the abstract.

pith-pipeline@v0.9.0 · 5773 in / 1680 out tokens · 50435 ms · 2026-05-25T10:38:16.666335+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We include the effect of cold dark baryons by scaling the measured mass in the atomic form by a factor of c in the mass budget of galaxies... mean value of c = 2.4±1.3
IndisputableMonolith/Foundation/DimensionForcing.lean alexander_duality_circle_linking unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We find no correlation between the MOND critical acceleration a0 and the central surface brightness of the stellar disk, μ3.6. This supports a0 being a universal constant for all galaxies.

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