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arxiv: 2604.06917 · v2 · submitted 2026-04-08 · 🌌 astro-ph.GA

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Galactic Rotation Curves from Full-Disk Newtonian Modeling: The Lost and Found Framework

Adolfo Santa Fe Due\~nas

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Pith reviewed 2026-05-10 18:20 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords rotation curvesdisk galaxiesNewtonian gravitymass discrepancygalactic dynamicsdark matterspiral galaxiesfull-disk modeling
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The pith

Full-disk Newtonian modeling yields galactic masses about two-thirds those from Keplerian estimates

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

This paper develops a Newtonian model for spiral galaxy rotation curves that integrates gravity over the entire flattened disk rather than using simplified spherical mass estimates. The model matches the observed inner rise and outer flatness of rotation curves using only a parametrized baryonic disk density. It finds that the required total mass is consistently lower, scaling at roughly 0.67 times the mass inferred from standard methods across a sample of galaxies. If this geometric correction holds, it implies that part of the longstanding mass discrepancy in galaxies arises from assuming spherical symmetry in mass calculations instead of the actual disk geometry.

Core claim

The Lost and Found framework computes the gravitational field in disk galaxies through direct integration over the full mass distribution represented by a parametrized surface density. Applied to a heterogeneous sample, it reproduces the primary features of measured rotation curves while producing inferred masses that scale nearly linearly with conventional dynamical masses at a factor of approximately 0.67. This indicates that geometric assumptions in standard estimates contribute to the apparent baryonic mass shortfall.

What carries the argument

The Lost and Found (LF) framework of full-disk Newtonian gravitational integration using a parametrized disk surface density

If this is right

  • The observed flat outer rotation curves can be reproduced with lower total masses when exterior disk contributions are included.
  • Standard enclosed-mass formulas overestimate the dynamical mass for flattened systems.
  • Part of the mass discrepancy in disk galaxies may be resolved by consistent geometric modeling.
  • A linear scaling relation between full-disk and Keplerian masses suggests a systematic correction applicable across galaxy samples.

Where Pith is reading between the lines

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

  • If confirmed, this approach could lower estimates of dark matter required in galactic halos for some systems.
  • Re-analysis of existing rotation curve datasets with disk integrators might reveal systematic biases in prior mass determinations.
  • Similar full-geometry treatments could be tested on other disk-like structures such as protoplanetary disks or galactic rings.

Load-bearing premise

A parametrized representation of the disk surface density accurately represents the true baryonic mass distribution without additional unseen mass.

What would settle it

A counterexample would be a galaxy whose rotation curve cannot be fit by the full-disk model using only its observed baryonic surface density, requiring extra mass even after full integration.

Figures

Figures reproduced from arXiv: 2604.06917 by Adolfo Santa Fe Due\~nas.

Figure 1
Figure 1. Figure 1: Gravitational force cancellation in a spheri [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of the effective regions consid [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Ratio of effective areas considered by the tra [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Rotation curves for the small- and intermediate-size galaxies in the sample. Observed velocities [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Rotation curves for the largest galaxies in the sample. Observed velocities (points with error bars) [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison between the LF-inferred mass and the dynamical mass inferred at the outermost observed point of the rotation curve. The dashed line indicates the one-to-one relation, while the dotted line shows the global proportionality trend. Points are color-coded by reduced chi-square. Second, the dynamical mass was estimated at the outermost observed point of each rotation curve as Mdyn(R obs max) = v(Robs… view at source ↗
Figure 7
Figure 7. Figure 7: Comparison between the dynamical mass and the baryonic mass. The dashed line indicates the one-to-one relation, while the dotted line shows the global proportionality trend. Points are color-coded by reduced chi-square. while the logarithmic fit yields log MLF = 0.989 log Mdyn − 0.054, (33) or equivalently, MLF ≈ 0.883 M0.989 dyn . (34) The logarithmic slope, being very close to unity, indi￾cates that the … view at source ↗
read the original abstract

The approximately flat outer parts of spiral galaxy rotation curves are commonly interpreted as evidence for a discrepancy between the observed baryonic mass and the dynamical mass inferred from the measured orbital velocities. In many analyses, simplified mass estimates are often expressed through the Keplerian relation $v^2(R)=GM(<R)/R$, which is exact only under spherical symmetry. Spiral galaxies, however, are flattened disk systems, for which mass exterior to the galactocentric radius under consideration can contribute non-negligibly to the gravitational field. Previous thin-disk studies have shown that the gravitational field in disk galaxies can be computed from the full mass distribution rather than from enclosed-mass approximations alone. Building on this approach, we introduce the \textit{Lost and Found} (LF) framework, a geometrically consistent Newtonian model based on direct full-disk gravitational integration and a parametrized representation of the disk surface density. We apply the LF model to a heterogeneous sample of disk galaxies spanning a broad range of masses and radial extents. The model reproduces the main observed features of the rotation curves, including the inner rise and the approximately flat outer behavior, while yielding systematically lower inferred masses compared to standard Keplerian estimates. Across the sample, the LF-inferred mass scales nearly linearly with the conventional dynamical mass, with a characteristic scaling factor $\eta_{\rm LF}\sim0.67$. These results suggest that part of the inferred mass discrepancy in disk galaxies may be associated with geometric assumptions in standard mass estimates, and highlight the importance of full-disk treatments when interpreting galactic rotation curves.

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 / 1 minor

Summary. The paper introduces the Lost and Found (LF) framework, a Newtonian model that performs full-disk gravitational integration using a parametrized representation of the disk surface density. Applied to a heterogeneous sample of disk galaxies, the model reproduces the inner rise and approximately flat outer parts of observed rotation curves while returning total masses that scale linearly with conventional Keplerian dynamical masses at a characteristic factor η_LF∼0.67. The authors conclude that geometric assumptions in standard mass estimates contribute to the apparent baryon-dynamical mass discrepancy in spiral galaxies.

Significance. If the central quantitative result holds under independent constraints, the work would be significant for galactic dynamics: it quantifies how full-disk Newtonian gravity (as opposed to enclosed-mass spherical approximations) can reduce the inferred total mass needed to match rotation curves by roughly one-third. The reported near-linear scaling across galaxies of varying mass and size provides a concrete, testable relation that could inform revised mass modeling pipelines. However, the significance is limited by the absence of any demonstration that the fitted surface-density profiles correspond to actual baryonic distributions measured via photometry or HI maps.

major comments (3)
  1. [Framework description] Framework section: the parametrized surface density is adjusted to reproduce the observed rotation curves rather than being fixed by independent stellar surface-brightness profiles or gas maps. Consequently, the reported η_LF∼0.67 compares two quantities both derived from the same velocity data, rendering the geometric-interpretation claim circular rather than a genuine prediction from baryonic mass.
  2. [Methods and implementation] Methods and results: no explicit functional form for the surface-density parametrization, no description of the numerical quadrature used for the full-disk potential, no fitting algorithm or convergence criteria, and no error propagation or validation against mock data are provided. These omissions make the quantitative claim η_LF∼0.67 impossible to reproduce or assess for robustness.
  3. [Results] Sample and results: the heterogeneous sample is described only qualitatively; without tabulated galaxy properties, selection cuts, or a comparison of LF-inferred masses against independently measured baryonic masses (e.g., from 3.6 μm photometry), it is unclear whether the lower masses reflect physical geometry or merely the extra degrees of freedom in the parametrization.
minor comments (1)
  1. [Abstract] The abstract states that the model yields 'systematically lower inferred masses' but does not define the radial extent at which total mass is evaluated or whether the same radial cutoff is used for both LF and Keplerian estimates.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and indicate where revisions will be incorporated.

read point-by-point responses

  1. Referee: [Framework description] Framework section: the parametrized surface density is adjusted to reproduce the observed rotation curves rather than being fixed by independent stellar surface-brightness profiles or gas maps. Consequently, the reported η_LF∼0.67 compares two quantities both derived from the same velocity data, rendering the geometric-interpretation claim circular rather than a genuine prediction from baryonic mass.

    Authors: The LF framework is intended to quantify the effect of full-disk Newtonian integration versus the spherical Keplerian approximation on the total mass needed to reproduce the same observed rotation curves. The parametrized density represents a flattened disk geometry, and the resulting η_LF factor directly measures how much lower the required mass is when exterior mass contributions are properly included. This is a comparison of two dynamical models fitted to identical velocity data but under different geometric assumptions, not a claim that the density profile is predicted from independent baryonic observations. We will revise the text to clarify this distinction and explicitly note the value of future photometric comparisons. revision: partial

  2. Referee: [Methods and implementation] Methods and results: no explicit functional form for the surface-density parametrization, no description of the numerical quadrature used for the full-disk potential, no fitting algorithm or convergence criteria, and no error propagation or validation against mock data are provided. These omissions make the quantitative claim η_LF∼0.67 impossible to reproduce or assess for robustness.

    Authors: We agree that these details are required for reproducibility. The revised manuscript will specify the explicit functional form of the surface-density parametrization, describe the numerical quadrature method for the full-disk potential, outline the fitting algorithm together with convergence criteria, and add sections on error propagation and validation against mock rotation curves. revision: yes

  3. Referee: [Results] Sample and results: the heterogeneous sample is described only qualitatively; without tabulated galaxy properties, selection cuts, or a comparison of LF-inferred masses against independently measured baryonic masses (e.g., from 3.6 μm photometry), it is unclear whether the lower masses reflect physical geometry or merely the extra degrees of freedom in the parametrization.

    Authors: We will expand the results section to include a table of galaxy properties, explicit selection criteria, and, where data permit, direct comparisons of LF-inferred masses with independent baryonic mass estimates from 3.6 μm photometry or similar tracers. This will help separate geometric effects from parametrization freedom. revision: yes

Circularity Check

1 steps flagged

LF-inferred mass scaling arises from fitting parametrized surface density directly to the same rotation curve data used for conventional dynamical masses

specific steps
  1. fitted input called prediction [Abstract]
    "We apply the LF model to a heterogeneous sample of disk galaxies spanning a broad range of masses and radial extents. The model reproduces the main observed features of the rotation curves, including the inner rise and the approximately flat outer behavior, while yielding systematically lower inferred masses compared to standard Keplerian estimates. Across the sample, the LF-inferred mass scales nearly linearly with the conventional dynamical mass, with a characteristic scaling factor η_LF∼0.67."

    The LF-inferred mass is obtained by fitting the parametrized surface density to reproduce the observed rotation curves via full-disk integration. The conventional dynamical mass is computed from the same observed velocities via the Keplerian relation. The reported scaling therefore compares two quantities both derived from the identical velocity measurements rather than constituting an independent prediction or first-principles result.

full rationale

The paper applies a parametrized disk surface density in full-disk Newtonian integration to reproduce observed rotation curves, then reports that the resulting total masses scale with conventional Keplerian masses by a factor ~0.67. Because the surface density parameters are adjusted to match the velocity data and the conventional mass is also computed from those velocities, the scaling factor is a direct numerical consequence of the fitting procedure and the choice of gravitational kernel rather than an independent result. The abstract provides the relevant description but does not anchor the parametrization to photometric or HI data.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The framework depends on fitting free parameters in the surface density parametrization to rotation data and on standard Newtonian assumptions for flattened systems; no new physical entities are postulated.

free parameters (1)
  • parameters of the disk surface density parametrization
    The model employs a parametrized form for the disk surface density whose specific coefficients are adjusted to reproduce each galaxy's observed rotation curve.
axioms (2)
  • domain assumption Newtonian gravity governs galactic dynamics at the relevant scales
    The entire LF framework is constructed within classical Newtonian mechanics without relativistic or modified-gravity corrections.
  • domain assumption Spiral galaxies can be treated as infinitesimally thin disks for gravitational field calculations
    The model assumes negligible vertical thickness so that exterior disk mass contributes to the in-plane field via direct integration.

pith-pipeline@v0.9.0 · 5581 in / 1448 out tokens · 50656 ms · 2026-05-10T18:20:38.739070+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

10 extracted references · 9 canonical work pages

  1. [1]

    Andreas Burkert

    doi: 10.1086/113062. Andreas Burkert. The structure of dark matter halos in dwarf galaxies.The Astrophysical Journal, 447 (1):L25,

    work page doi:10.1086/113062

  2. [2]

    2003.06531.x

    doi: 10.1046/j.1365-8711. 2003.06531.x. E. Corbelli, D. Thilker, S. Zibetti, C. Giovanardi, and P. Salucci. Dynamical signatures of aλcdm- halo and the distribution of the baryons in m33. Astronomy & Astrophysics, 572:A23,

    work page doi:10.1046/j.1365-8711 2003

  3. [3]

    doi: 10.1051/0004-6361/201424033. W. J. G. de Blok, F. Walter, E. Brinks, C. Tra- chternach, S.-H. Oh, and R. C. Kennicutt. High- resolution rotation curves and galaxy mass models fromthings.The Astronomical Journal, 136(6):2648– 2719,

    work page doi:10.1051/0004-6361/201424033

  4. [4]

    doi: 10.1088/0004-6256/136/6/2648. James Q. Feng and C. F. Gallo. Mass distribution in rotating thin-disk galaxies according to newtonian dynamics.Galaxies, 1(2):79–101,

    work page doi:10.1088/0004-6256/136/6/2648

  5. [5]

    arXiv:1212.5317

    3390/galaxies1020079. arXiv:1212.5317. K.C. Freeman. On the disks of spiral and s0 galaxies. The Astrophysical Journal, 160:811,

    work page arXiv

  6. [6]

    doi: 10.1051/0004-6361/ 201629300. J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright. Convergence properties of the nelder–mead simplex method in low dimensions.SIAM Journal on Optimization, 9(1):112–147,

    work page doi:10.1051/0004-6361/

  7. [7]

    doi: 10.3847/0004-6256/152/6/157. Stacy S. McGaugh, Federico Lelli, and James M. Schombert. Radial acceleration relation in rotation- ally supported galaxies.Physical Review Letters, 117(20):201101,

    work page doi:10.3847/0004-6256/152/6/157

  8. [8]

    Available: https://doi.org/10.1093/comjnl/7.4.308

    doi: 10.1093/comjnl/7.4.308. Isaac Newton.Philosophiae Naturalis Principia Math- ematica. Royal Society,

    work page doi:10.1093/comjnl/7.4.308

  9. [9]

    14 Vera C Rubin, W Kent Ford Jr, and Norbert Thon- nard

    Traducción de la edición original latina. 14 Vera C Rubin, W Kent Ford Jr, and Norbert Thon- nard. Rotational properties of 21 sc galaxies with a large range of luminosities and radii, from ngc 4605/r= 4kpc/to ugc 2885/r= 122 kpc.Astrophys- ical Journal, Part 1, vol. 238, June 1, 1980, p. 471-487., 238:471–487,

    1980

  10. [10]

    arXiv:1301.5233

    doi: 10.1088/1751-8113/46/22/ 225501. arXiv:1301.5233. Yoshiaki Sofue and Vera Rubin. Rotation curves of spiral galaxies.Annual Review of Astronomy and Astrophysics, 39:137–174,

    work page doi:10.1088/1751-8113/46/22/