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REVIEW 4 major objections 5 minor 89 references

A Novel Test for MOND: Gravitational Lensing by Disc Galaxies

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper argues that MOND predicts a substantially higher strong-lensing cross section for inclined disc galaxies than dark-matter halos fitted to the same rotation curves, a difference upcoming surveys should be able to detect.

desk verdict Solid MOND lensing calculation with an unsupported survey-level claim; the fix is to reframe the abstract, and the core is worth refereeing. read the letter →

arxiv 2411.17888 v2 pith:UK6RT7XH submitted 2024-11-26 astro-ph.GA astro-ph.COgr-qc

Christopher Harvey-Hawes , Marco Galoppo This is my paper · ORCID
classification astro-ph.GAastro-ph.COgr-qc
keywords ModifiedNewtoniandynamicsgravitationallensingdiscgalaxiesphantomdarkmatterquasi-linearMONDstrongcrosssectionalternativesinterpolatingfunction
topics Dark Matter
open problems Dark Matter
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper is trying to establish a falsifiable, survey-ready difference between MOND and the dark-matter picture: disc galaxies should act as much more efficient strong gravitational lenses in MOND, and the effect should grow strongly as the disc is seen more edge-on. The authors construct the equivalent Newtonian system for a realistic exponential disc plus bulge, compute the phantom dark matter distribution, and then apply standard lensing formalism. They find MOND-driven lensing cross sections that exceed dark-matter predictions fitted to the same rotation curve, and conclude that upcoming surveys will be able to distinguish the two paradigms simply by counting disc galaxy lenses.

What carries the argument

The central object is the phantom dark matter density distribution $\rho_{\rm ph} = \frac{1}{4\pi G}\,\vec{\nabla}\cdot[\tilde{\nu}(y)\,\vec{\nabla}\Phi_N]$ of quasi-linear MOND with $\tilde{\nu}(y) = -\frac12 + \sqrt{\frac14 + \frac1y}$. It converts MOND into an equivalent Newtonian system: the lensing potential is the Newtonian potential of the baryons plus the potential of this fictitious halo, so standard weak-field lensing applies. Because the PDM distribution inherits the disc's flattening and is strongly non-spherical, its projected surface density rises steeply with inclination, and that is what drives the predicted cross-section enhancement.

What would settle it

Count strong-lensing disc galaxies in Euclid or LSST, restrict the sample to inclinations above roughly 70 degrees, and compare the observed number density with the MOND and dark-matter predictions normalised to the same rotation curves; the paper's central claim fails if no high-inclination excess appears.

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Extended reading notes

Core claim

The paper contends that strong gravitational lensing by disc galaxies in MOND is dominated not by the baryonic disc alone but by the phantom dark matter (PDM) that quasi-linear MOND associates with that disc. For a realistic exponential disc with a Plummer bulge, the PDM forms a flattened, disc-like halo whose projection on the lens plane grows steadily with inclination, so the lensing cross section for a galaxy seen at 70 to 90 degrees is markedly larger than for a conventional non-singular isothermal dark halo fitted to the same rotation curve. From this the paper concludes that the standard realisation of MOND predicts a substantial excess of disc galaxy lenses, especially edge-on ones, relative to dark-matter-driven predictions in Euclid, DES and LSST, and that the sign of the correlations between lens parameters and cross section, for example the counter-intuitive decrease of cross section with increasing bulge mass, is itself a MOND signature.

Load-bearing premise

The entire lensing prediction rests on the assumption that the still-unknown relativistic version of MOND bends light exactly as general relativity does, but with the MOND gravitational potential replacing the Newtonian one.

Editorial extensions

If this is right

  • Under MOND, the number of disc galaxy lenses expected in Euclid, DES and LSST should be substantially larger than the dark-matter prediction, so a surplus of edge-on disc lenses would support MOND.
  • The inclination dependence of the lensing cross section is steeper in MOND than for a spherical dark halo, making the inclination distribution of lenses a second observable discriminator.
  • Within the tested parameter ranges, increasing bulge mass decreases the MOND lensing cross section, the opposite of standard weak-field lensing expectations, so the sign of the mass-cross-section correlation is itself a test.
  • Disc galaxy lensing, combined with rotation-curve data, could constrain the MOND interpolating function because lensing probes the transition acceleration regime.
  • The two choices of interpolating function tested in the paper give nearly identical lensing signatures, so the predicted excess over dark matter is not an artefact of that one choice.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An unstated consequence is that existing strong-lens samples with measured disc inclinations may already contain enough edge-on lenses to start probing the trend before the next generation of surveys is complete.
  • The framework could be carried over to other flattened baryonic systems, such as edge-on S0 galaxies, where the phantom disc should similarly boost the lensing cross section.
  • The predicted anti-correlation between bulge mass and lensing cross section means that morphology-dependent selection effects must be controlled in any survey comparison, since MOND prefers lensing by bulge-poor, high-inclination discs.
  • External field effects, neglected here for isolated galaxies, should modulate the enhancement in group or cluster environments and could provide a further, environment-dependent test of the scenario.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper presents a QUMOND-based calculation of strong gravitational lensing by isolated disc galaxies. The authors model the baryonic mass as a thick exponential disc plus a Plummer bulge, construct the equivalent Newtonian system with the phantom dark matter density of Eq. (7), and compute deflection angles, magnifications, shear, critical curves, caustics, and the lensing cross-section σ as a function of inclination. They compare σ for a template galaxy with an NSIS dark-matter halo fitted to the same MOND rotation curve (Fig. 8), and they test two interpolating functions. The abstract and Section 5 conclude that MOND predicts a substantially larger number of disc-galaxy lenses in Euclid, DES, and LSST, making MOND distinguishable from dark matter, and that disc-galaxy lensing can constrain the MOND interpolating function.

Significance. The forward-modeling machinery is in several respects a step forward: it uses realistic exponential disc profiles rather than idealized Mestel/Kuzmin discs, it derives the phantom dark matter distribution for a disc+bulge system, it makes the lensing code publicly available, and it checks robustness to the interpolating function in Appendix B. The fixed-dynamics comparison to a dark-matter halo fitted to the same rotation curve is a fair way to isolate the lensing prediction at given circular velocity. However, the headline result—a detectable increase in number counts—does not follow from the quantity computed. The cross-section σ in Figs. 6–8 is the area inside the tangential caustic for point sources only, and the paper itself states in Section 2 that σ is survey-independent and does not specialize to any survey. No convolution with galaxy luminosity or velocity functions, inclination distributions, source redshift distributions, or survey selection functions is performed. The manuscript therefore provides a plausible cross-section calculation but not yet a test that can be compared with Euclid, DES, or LSST.

major comments (4)
  1. [§2, §5, Abstract] The central claim of the abstract and Section 5—that MOND predicts a substantial increase in the number count of disc-galaxy lenses and is distinguishable from dark matter in upcoming surveys—is not derived anywhere in the paper. Section 2 explicitly defines σ as a survey-independent quantity and states that the lensing likelihood 'will be influenced by the specific observations carried out' and that the authors 'do not specialise to any specific surveys.' No subsequent step connects σ to a detection rate: there is no integration over the disc-galaxy mass or velocity function, no inclination distribution, no source redshift distribution, no source counts, no magnification bias, and no survey selection function. Figure 8 alone cannot support the number-count statement, and this is a load-bearing gap rather than a presentation issue.
  2. [§2, Figs. 6–8] The cross-section used in the comparison is only the area enclosed by the tangential caustic for point sources. For a near-axisymmetric projected mass distribution the tangential caustic degenerates to a point, so its area vanishes; this is consistent with Figs. 6–8 being restricted to i = 70°–90°. The standard strong-lensing cross-section for producing multiple images includes the area inside the radial caustic (two-image systems), which does not vanish at lower inclinations. The MOND-vs-DM comparison in Fig. 8 therefore compares only four-image cross-sections of nearly edge-on discs. Even if every computed point is correct, this restricted quantity does not measure the total lensing probability for disc galaxies, so the global claim of a MOND excess in lens number counts is not established.
  3. [§4, after Eq. (23)] The statement that 'changing the DM halo profile does not affect the lensing cross section in a relevant manner if we maintain a normalization' is asserted without a supporting calculation. Only one NSIS profile, fitted to one MOND rotation curve, is shown (Fig. 9). To claim distinguishability from dark matter, the authors should test at least a cuspy NFW and a cored profile with parameters spanning the observational scatter, and report the resulting range of σ. Without this, the robustness of the DM comparison is unquantified.
  4. [Footnote 1, Abstract, §5] The entire lensing calculation assumes that the deflection angle is given by the standard weak-field formula of general relativity with the QUMOND potential in place of the Newtonian potential. Footnote 1 explicitly acknowledges that this restricts the possible relativistic MOND extension, and that different theories (e.g., TeVeS) can change the deflection law. Since the abstract and Section 5 present the number-count excess as a property of 'MOND' without carrying this caveat, the claim is stronger than what has been computed. Moving this assumption into the main text and qualifying the conclusions accordingly is necessary.
minor comments (5)
  1. [§3.2, Fig. 6] The text specifies zd ∈ {0.35, 0.105, 0.035} kpc, but the Fig. 6 legend lists zd = 0.04, 0.1, 0.35 kpc; these values should be reconciled.
  2. [Appendix A.2] Equations (A7) and (A8) both label the deflection component as αξ1; the second equation should define αξ2.
  3. [Fig. 10 caption] The caption reads 'a Plummer profile (M ⊙, and rb = 0.7 kpc)', with the mass value apparently missing; please supply the value used.
  4. [Appendix A and Acknowledgements] The GitHub URL is given as 'https://github.com/chrisharhaw/MOND lensing.git', which contains a space and is not a valid URL; please provide a working repository address.
  5. [§2] The sentence stating that extended sources 'will have higher lensing likelihood, but ... point-like sources is sufficient' is too terse given the survey-level claims; please explain how source-size effects would enter the number-count comparison or state explicitly that they are neglected.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the MOND lensing cross-sections are derived forward from QUMOND with literature inputs, and the dark-matter comparison is normalized at fixed rotation curve rather than fitted to the lensing result.

full rationale

The derivation chain is self-contained. Baryonic density profiles (Plummer bulge plus exponential disc, Eqs. 14-17) are inputs; the QUMOND equations (6)-(7) with the literature interpolating function (21) produce the phantom dark matter distribution; the standard lensing equations (9)-(13) then yield deflection, caustics, and the cross section sigma. No fitted parameter is renamed as a prediction: the NSIS halo is explicitly fitted to the MOND rotation curve through Eq. (23), and the lensing cross-sections in Fig. 8 are subsequently computed from that halo, so the MOND-versus-DM difference is a derived consequence of the assumed spherical halo geometry rather than an input. The cited prior results (QUMOND, the Phantom of Ramses interpolation, and Keeton & Kochanek disc-lensing formalism) are external and not author-self citations, and the two self-citations (Galoppo & Wiltshire 2024; Galoppo et al. 2024) appear only in a list of alternative gravity models and carry no load. Footnote 1 openly flags the assumption that the lensing potential is twice the Newtonian potential; this is a stated modeling assumption, not a circular reduction. The abstract's number-count claim is broader than the computed survey-independent sigma, and Section 2 explicitly notes that sigma is survey-independent and that the paper does not specialize to specific surveys; this is an unquantified extrapolation rather than a step that reduces to its own inputs. No circular step is therefore identified.

Assumptions & free parameters 7 free parameters · 7 assumptions · 0 invented entities

The central claims rest on the QUMOND model, the chosen interpolating function, and a set of representative galaxy parameters; the only numbers fitted to data in this work are the two NSIS halo parameters used for the dark-matter comparison. The galaxy parameters are physically motivated prior inputs, not fitted constants.

free parameters (7)
  • Disc mass Md = 1e11 Msun
    Chosen by hand to represent a massive spiral following Keeton & Kochanek (1998); affects all lensing predictions.
  • Disc scale length Rd = 3.5 kpc
    Chosen by hand following Keeton & Kochanek (1998); affects the projected density and cross-sections.
  • Disc scale height zd = 0.35, 0.105, 0.035 kpc (three values)
    Chosen so that zd/Rd = {0.1, 0.03, 0.01} following Keeton & Kochanek (1998); used to study thickness effects on the cross-section.
  • Bulge mass Mb = 1e9, 1e10, 2e10 Msun
    Chosen to span realistic bulge-to-disc ratios; used to study bulge mass effects on the cross-section.
  • Bulge scale radius rb = 0.105, 0.35, 0.7 kpc (rb/Rd = 0.03, 0.1, 0.2)
    Chosen from morphological correlations; affects the baryonic potential and the PDM distribution.
  • NSIS halo central density rho0 = 6.36e7 Msun/kpc^3
    Fitted so that the DM-baryon rotation curve matches the MOND rotation curve (Section 4); this normalization determines the DM lensing cross-section in the comparison.
  • NSIS halo core radius r0 = 3.44 kpc
    Second parameter of the fit to the MOND rotation curve; determines the DM lensing cross-section in the comparison.
assumptions (7)
  • domain assumption QUMOND is a valid approximation to AQUAL MOND, allowing construction of the equivalent Newtonian system via Eq. (7).
    Taken from Milgrom (2010); the paper uses QUMOND rather than the full AQUAL equation.
  • domain assumption The lensing potential equals twice the Newtonian potential of the equivalent Newtonian system, as in general relativity.
    Stated in footnote 1, Section 2; restricts the possible relativistic MOND extension.
  • domain assumption The interpolating function is nu-tilde(y) = -1/2 + sqrt(1/4 + 1/y).
    Equation (21), from Lughausen et al. (2015); robustness checked with the RAR function in Appendix B.
  • domain assumption The lens is isolated; external field effects are neglected.
    Stated in Section 1; acknowledged to be a stronger requirement in MOND than in the DM scenario.
  • domain assumption A flat Lambda-CDM cosmology with Omega_m0 = 0.3, H0 = 70, zL = 0.5, zS = 2.0 provides the background geometry.
    Stated in Section 1; assumed as a first-order approximation to an unknown MOND cosmology.
  • domain assumption The algebraic MOND rotation curve formula vROT = sqrt(R[1 + nu-tilde(y)] |dPhi_N/dR|) is valid on the galactic plane.
    Equation (23), from Banik et al. (2018); used to normalize the DM halo to the MOND rotation curve.
  • standard math The disc scale height is constant with radius.
    Section 3.1, following observed photometry of edge-on galaxies (van der Kruit & Searle 1981, 1982).

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Cite this review

Pith. "Pith review of A Novel Test for MOND: Gravitational Lensing by Disc Galaxies." pith.science (2026). https://pith.science/paper/UK6RT7XH

@misc{pith2026241117888,
  author       = {Pith},
  title        = {Pith review of: A Novel Test for MOND: Gravitational Lensing by Disc Galaxies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UK6RT7XH}},
  note         = {Machine review of arXiv:2411.17888}
}
read the original abstract

Disc galaxies represent a promising laboratory for the study of gravitational physics, including alternatives to dark matter, owing to the possibility of coupling rotation curves' dynamical data with strong gravitational lensing observations. In particular, Euclid, DES and LSST are predicted to observe hundreds of thousands of gravitational lenses. Here, we investigate disc galaxy strong gravitational lensing in the MOND framework. We employ the concept of equivalent Newtonian systems within the quasi-linear MOND formulation to make use of the standard lensing formalism. We derive the phantom dark matter distribution predicted for realistic disc galaxy models and study the impact of morphological and mass parameters on the expected lensing. We find purely MONDian effects dominate the lensing and generate non-trivial correlations between the lens parameters and the lensing cross section. Moreover, we show that the standard realisation of MOND predicts a substantial increase in the number count of disc galaxy lenses compared to the dark matter-driven predictions, making it distinguishable from the latter in upcoming surveys. Finally, we argue that disc galaxy gravitational lensing, coupled to additional astronomical observations, can be used to constrain the interpolating function of MOND.

Figures

Figures reproduced from arXiv: 2411.17888 by the authors.

Figure 1
Figure 1. Lensing configuration for SGL by a disc galaxy. We report source, lens and observer positions, as well as the relevant angles and coordinate systems. Here, α is the deflection angle, β is the angular source position and θ is the angular image position. Therefore, to characterise the inclination effects of disc galaxies in MOND we only consider σ as an indirect measure of SGL likelihood and do not specialise to any s… view at source ↗
Figure 2
Figure 2. PDM density distribution on the x − z plane (upper panel) and on the x−y plane (lower panel) for a disc galaxy with Md = 1011 M⊙, Rd = 3.5 kpc, zd = 0.35 kpc, Mb = 109 M⊙, and rb = 0.7 kpc. A log-scale is used for the density to highlight the morphology of the PDM distribution. Finally, from [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Ratio of the baryon density to the PDM den￾sity, ρB/ρph, along the radial direction on the equatorial plane (top panel), and the corresponding two-dimensional distribution in the x − z plane within a scale height of the galactic disc (bottom panel) for a disc galaxy with Md = 1011 M⊙, Rd = 3.5 kpc, zd = 0.35 kpc, Mb = 109 M⊙, and rb = 0.7 kpc. The purple dashed line in the top panel highlights the point at which the… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Example of lensing observables, namely the deflection angle (α), the magnification (µ), and the shear (γ), for a disc galaxy of inclinations i = 0 (left) and i = π/2 (right). The disc galaxy model is obtained by fixing Md = 1011 M⊙, Rd = 3.5 kpc, zd = 0.35 kpc, Mb = 10…
Figure 5
Figure 5. Figure 5: Example image configurations, caustic curves and critical curves for spiral galaxy MOND lenses with varying inclination and point source objects placed at a constant position relative to the lens centre. The solid black line, dotted red line and dashed-dotted red-line …
Figure 6
Figure 6. Figure 6: Impact of disc thickness zd on lensing cross section σ with varying inclination angle within the MOND scenario. The other corresponding lens galaxy parameters are Md = 1011 M⊙, Rd = 3.5 kpc, Mb = 109 M⊙, and rb = 0.7 kpc. The lens and source are placed at redshift zL =…
Figure 7
Figure 7. Figure 7: Impact of bulge mass Mb on lensing cross section σ with varying inclination angle within the MOND scenario. The other corresponding lens galaxy parameters are Md = 1011 M⊙, Rd = 3.5 kpc, zd = 0.35 kpc, and rb = 0.7 kpc. The lens and source are placed at redshift zL = 0…
Figure 8
Figure 8. Figure 8: A comparison of lensing cross sections predictions with varying inclination angle for the same disc galaxy in MOND and the conventional DM scenario. The disc galaxy parameters are Md = 1011 M⊙, Rd = 3.5 kpc, zd = 0.35 kpc, and Mb = 109 M⊙, and rb = 0.7 kpc. The DM halo…
Figure 9
Figure 9. Figure 9: A comparison of MONDian rotation curve predictions with the best fit DM alternative. The solid blue line shows the MONDian rotation curve prediction for a disc galaxy with parameters: Md = 1011 M⊙, Rd = 3.5 kpc, zd = 0.35 kpc, and Mb = 109 M⊙, and rb = 0.7 kpc. The das…
Figure 10
Figure 10. Figure 10: A comparison between the numerically obtained PDM (black line) and analytical prediction (dashed purple line) for a Plummer profile with M⊙, and rb = 0.7 kpc. The MOND interpolating function selected is the one displayed in Eq. (21). The second intergal in Eq. (A6) is…
Figure 11
Figure 11. Figure 11: PDM densities ratio, ρph-RAR/ρph-S on the z −x plane (left panel) and on the x−y plane (right panel), respectively, for a disc galaxy with Md = 1011 M⊙, Rd = 3.5 kpc, zd = 0.35 kpc, Mb = 109 M⊙, and rb = 0.7 kpc. 70.0 72.5 75.0 77.5 80.0 82.5 85.0 87.5 90.0 i [deg] 0.…
Figure 12
Figure 12. Figure 12: A comparison of the effects of varying inclination on the SGL cross section produced for the interpolating function used throughout this work, the RAR function, and the DM halo alternative. The disc galaxy parameters are Md = 1011 M⊙, Rd = 3.5 kpc, zd = 0.35 kpc, and …

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