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REVIEW 3 major objections 6 minor 59 references

Modified Gravity Theories in Light of the Anomalous Velocity Dispersion of NGC1052-DF2

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read NGC1052-DF2, the galaxy claimed to have no dark matter, still fits MOND, MOG, Weyl conformal gravity, and general relativity without dark matter, with only emergent gravity failing at the 20 Mpc distance.

desk verdict A useful but flawed consistency check: the chi-squares that carry the main claim are never defined, and the 'fully consistent' abstract oversells emergent gravity's poor fit. read the letter →

arxiv 1908.07160 v2 pith:AWN5QOHE submitted 2019-08-20 gr-qc astro-ph.COastro-ph.GA

Tousif Islam , Koushik Dutta This is my paper · ORCID
classification gr-qcastro-ph.COastro-ph.GA
keywords NGC1052-DF2ultra-diffusegalaxyvelocitydispersionmodifiedgravityMONDMOG/STVGWeylconformalemergent
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

The paper asks whether NGC1052-DF2, an ultra-diffuse galaxy whose low globular-cluster velocity dispersion has been interpreted as evidence that it contains essentially no dark matter, actually challenges modified gravity theories. Starting from a Sersic stellar mass profile and solving the spherically symmetric Jeans equation, the authors compute the expected line-of-sight velocity dispersion for general relativity without dark matter, MOND with and without the external-field effect, MOG/STVG, Weyl conformal gravity, and emergent gravity. At the usual assumed distance of 20 Mpc, every model except emergent gravity falls within the observed confidence intervals, with reduced chi-square values from 1.47 to 5.00; emergent gravity gives 9.99. At the disputed nearer distance of 13.2 Mpc, all six models fit, with chi-square values between 1.79 and 4.55. The paper concludes that the galaxy's low dispersion does not falsify modified gravity and can also be explained by baryons alone under general relativity.

What carries the argument

The central object is the projected line-of-sight velocity dispersion obtained from the isotropic, spherically symmetric Jeans equation: $\sigma^2(r) = \frac{1}{\rho(r)}\int_r^\infty \rho(r') a(r')\,dr'$ and $\sigma_{\mathrm{LOS}}^2(R) = \frac{\int_R^\infty r\,\sigma^2(r)\rho(r)/\sqrt{r^2-R^2}\,dr}{\int_R^\infty r\,\rho(r)/\sqrt{r^2-R^2}\,dr}$. Into this equation the authors feed the truncated Sersic stellar density of Eq. (2.1) and each theory's acceleration law: MOND's interpolation function with $a_0=1.21\times10^{-10}$ m/s$^2$, Weyl conformal gravity's fourth-order acceleration with constants $R_0=24$ kpc, $M_0=5.6\times10^{10}\,M_\odot$, $\kappa=9.54\times10^{-54}$ cm$^{-2}$, MOG's vector-field acceleration with $\alpha=1.30$, $\mu=0.443$ kpc$^{-1}$, and emergent gravity's extra term $a_v = a_0 M(r)/[d(M(r)r)/dr]$. The Jeans pipeline converts each theory's acceleration into a dispersion curve that can be compared with the ten globular-cluster velocities.

What would settle it

A decisive check would be an independent distance measurement for NGC1052-DF2 (for example from the tip of the red-giant branch) plus a stellar mass profile from resolved star counts, along with radial velocities for at least thirty globular clusters. Recomputing the six predicted dispersion profiles from that measured mass profile, the consistency claim is falsified if the observed line-of-sight dispersion is excluded at 2σ by all of the baryons-only predictions in any radial bin.

Watch

Extended reading notes

Core claim

On the paper's own terms, the finding is that the ten globular-cluster velocity dispersions of NGC1052-DF2 are consistent with the baryonic mass alone, both in general relativity without dark matter and in most modified gravity theories. The quantitative ranking is distance-dependent: for D=20 Mpc the reduced chi-square values are 1.82 for GR, 1.47 for MOG, 3.60 for MOND, 2.01 for MOND with the external-field effect, 5.00 for Weyl conformal gravity, and 9.99 for emergent gravity; for D=13.2 Mpc they improve to 2.04, 1.81, 1.89, 1.79, 3.35, and 4.55, respectively. The authors trace emergent gravity's poor 20-Mpc performance to its additional acceleration term, which is two to three orders of magnitude above the Newtonian value in the inner galaxy. They extend the conclusion to NGC1052-DF4, a second claimed dark-matter-free galaxy, whose predicted rms dispersions are compatible with most of the same theories at the 2σ level.

Load-bearing premise

The load-bearing premise is that the visible stellar mass is well described by a truncated Sersic profile with the adopted central surface density, effective radius, and cutoff radius (and either the 20 or 13.2 Mpc distance); if the true stellar profile, tidal truncation, or distance differs, every predicted dispersion curve shifts and the reported chi-square rankings change.

Editorial extensions

If this is right

  • A dark-matter-free interpretation of NGC1052-DF2 does not discriminate between general relativity plus baryons and modified gravity: the same stellar mass profile reproduces the data in both paradigms.
  • If the galaxy is at 13.2 Mpc, the data become compatible with all six models considered, so a decisive distance measurement would settle which model rankings matter.
  • MOG's good fit is aided by its mass-dependent parameters $\alpha$ and $\mu$, which give it a flexibility the other modified theories lack.
  • At 20 Mpc, emergent gravity is the only theory examined that fails to match the data, because its extra acceleration term dominates the baryonic Newtonian acceleration in the inner galaxy.
  • The external-field effect improves MOND's fit at 20 Mpc from 3.60 to 2.01, and the true MOND prediction with a realistic external acceleration lies between those values.

Reading between the lines

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

  • With only ten tracers and asymmetric error bars, the reduced chi-square differences among the better-fitting models (1.47–3.60 at 20 Mpc) may not be statistically distinguishable; a full likelihood treatment could make several models essentially equivalent.
  • The sharp truncation radius is a simplified proxy for tidal stripping; a theory-specific tidal-radius calculation would alter the outer parts of every predicted profile and could reorder the chi-square ranking.
  • The same Jeans-profile pipeline could be applied to other ultra-diffuse galaxies discovered in wide surveys; a galaxy whose measured dispersion lies well below the baryon-only prediction would be the real falsification test that DF2 does not provide.
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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

3 major / 6 minor

Summary. The paper computes line-of-sight velocity dispersion profiles for the ultra-diffuse galaxy NGC1052-DF2 under general relativity without dark matter, MOND (with and without an external field effect), Weyl conformal gravity, MOG, and Verlinde's emergent gravity, using a Sérsic baryonic mass model at two assumed distances (20 Mpc and 13.2 Mpc). It reports reduced chi-square values comparing predicted dispersion profiles with ten globular-cluster velocity data points and concludes that the data are fully consistent with GR and with all modified gravity theories except emergent gravity at 20 Mpc. It also gives rms dispersion predictions for NGC1052-DF4. The quantitative evidence for the central claim is in Section V: Tables I and II contain reduced chi-square values, and Figure 4 compares rms dispersion bounds.

Significance. If the statistical comparison were valid, the paper would be a useful unified reference for how four modified gravity theories plus GR fare against the DF2 data, with the strength of treating both disputed distance estimates and including MOND's external field effect. The authors are transparent about MOG's parameter flexibility and about idealizations such as spherical symmetry, isotropy, and a sharp truncation radius. However, the central claim rests entirely on chi-square values whose definition is never given; since individual globular-cluster velocities are not dispersion measurements, the quoted numbers cannot be verified as stated. The paper also does not propagate uncertainties from the mass model, distance, or truncation radius into the chi-square tables. The comparison is therefore not yet a sound basis for the abstract's 'fully consistent' conclusion.

major comments (3)
  1. [Section V, Tables I and II] The reduced chi-square values in Tables I and II are the sole quantitative evidence for the abstract's central claim that the dispersion data of NGC1052-DF2 are 'fully consistent' with the modified gravity paradigm, yet the manuscript never defines how χ²/dof is computed from the ten globular-cluster velocities. A single line-of-sight velocity v_i is one draw from the velocity distribution at projected radius R_i, not a measurement of σ_los(R_i); if Figure 2's 'individual GC velocity dispersion measurements' are the absolute values |v_i| plotted against the predicted σ_los curve, the test is biased because under a Gaussian the expectation of |v| is about 0.80σ. The authors must state the exact statistic, report the ten input velocities, and either use a Gaussian likelihood such as ∏_i N(v_i | 0, σ_los^2(R_i) + ε_i^2) or bin the data into dispersion estimates with proper errors. Without this, the numbers in Tables I and II cannot be checked and the consistency claim is unverified.
  2. [Section IIIc and Section VI] The MOG parameters α = 1.30 and μ = 0.443 kpc⁻¹ are taken from Moffat and Toth [44], who fit the velocity dispersion of NGC1052-DF2 itself; the MOG row in Tables I and II is therefore a same-galaxy re-fit rather than an independent prediction. The paper explicitly acknowledges in Section VI that MOG 'enjoys one additional degree of freedom' because its parameters are mass-dependent. To make the comparison meaningful, the authors should either fix MOG parameters from external galaxy samples or apply a model-comparison penalty (e.g., AIC or BIC) for the fitted parameters. As presented, the lower MOG χ² relative to MOND, Weyl, and Emergent gravity does not by itself establish that MOG is more consistent with the data.
  3. [Section V, Eq. (5.2) and Figure 4; Section VI] The error bars in Figure 4 are obtained by varying the effective radius by 50%, but Tables I and II are computed with fixed values of Re, Σ0, rcut, and anisotropy, with no propagation of these uncertainties or of the distance uncertainty into the predicted σ_los profiles. Since the distance is disputed (20 Mpc vs 13.2 Mpc) and rcut is a hand-chosen truncation, the claimed consistency should be demonstrated by showing how χ² changes under these variations, not only by the two distance rows in Tables I and II. The statement in Section VI that the simplifications 'would unlikely to alter the final conclusion much' is an assertion that needs quantitative support.
minor comments (6)
  1. [Throughout, Section IIIa] The galaxy parameter is spelled 'Sersic' in Section II but should be 'Sérsic' throughout; the phrase 'Modified Newtonian Dynamcies' in the title and Section IIIa should be 'Modified Newtonian Dynamics'.
  2. [Abstract] The abstract contains a duplicated article: 'coupled to the the baryonic mass' should read 'coupled to the baryonic mass'.
  3. [Section IIIb, Eq. (3.3)] The exterior moment E_{-1}(r) appears in Eq. (3.3) but is not explicitly defined; the given definition of E_n(r) covers n = -1 only implicitly, and this should be stated.
  4. [Figures 2 and 5] The captions refer to 'individual GC velocity dispersion measurements' for the blue points; if these points are the original individual radial velocities, they should be relabeled as such and the error bars explained, because individual velocities are draws from a distribution, not dispersion measurements.
  5. [Section V, Tables I and II] The degrees of freedom for the quoted χ²/dof are never stated; the authors should specify dof for each theory, for example as the number of globular clusters minus the number of free parameters in the model.
  6. [Section V, data availability] The ten globular-cluster velocities and their uncertainties used in Figures 2 and 5 are not tabulated in the manuscript; adding a data table would make the analysis reproducible and allow readers to verify the chi-square construction.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the dispersion predictions are derived from an externally fitted stellar mass profile and fixed theory parameters, not from the target dispersion data.

full rationale

The paper's derivation chain is: (i) adopt the Sersic mass density of Eq. (2.1), originally fit to surface photometry by van Dokkum et al. and approximated by Moffat and Toth; (ii) insert the baryonic acceleration predicted by each theory (MOND Eq. 3.2, Weyl Eq. 3.3, MOG Eq. 3.4, Emergent Eq. 3.5); (iii) solve the isotropic Jeans equation (Eq. 4.2) and project (Eq. 4.3); (iv) compare to the 10 GC velocity data through reduced chi-square. The MOG parameters alpha=1.30 and mu=0.443 kpc^-1 are adopted from Moffat and Toth [44] via the mass-dependent scaling relations of Moffat and Toth [49], not fitted to DF2's dispersion in this paper; the text explicitly contrasts these with rotation-curve values and notes MOG's extra degree of freedom. This is a parameter choice, not a circular prediction. MOND, Weyl, and Emergent use fixed or externally calibrated constants (a0, R0, M0, kappa). No uniqueness theorem or author-imported ansatz bears the argument; self-citations [28,35] appear only in the introduction's literature survey. The paper does not define the chi-square statistic used in Tables I and II, which is a reproducibility and statistical-validity concern (comparing absolute velocities to sigma_los would bias residuals), but that is not a circularity of the derivation chain. The modeling assumptions (spherical symmetry, isotropy, rcut, inclination) are stated as caveats and do not smuggle the conclusion in.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a fixed baryonic mass model, theory parameters imported from earlier fits, and several explicit modeling choices (truncation radius, isotropy, external field strength). The MOG parameters are the most concerning because they were calibrated for the same galaxy in a prior paper, reducing the strength of the MOG consistency test.

free parameters (6)
  • MOG alpha = 1.30
    Dedicated strength parameter for the target galaxy, inherited from Moffat and Toth 2018; not a global constant, and the paper notes this extra flexibility.
  • MOG mu = 0.443 kpc^-1
    Range parameter for the vector field in MOG, from the same-galaxy prior analysis; appears in Eq. 3.4.
  • Sersic Sigma0 = 1.25e7 Msun/kpc^2
    Characteristic surface density in the approximate mass profile Eq. 2.1, fitted to photometry in prior literature.
  • Effective radius Re = 2.0 kpc (D=20) / 1.4 kpc (D=13.2)
    Determines the mass profile and is distance-dependent; taken from Sersic fits in refs [1] and [9].
  • Truncation radius rcut = 10 kpc (D=20) / 8 kpc (D=13.2)
    Hand-chosen sharp trimming radius to mimic tidal stripping; affects the outer dispersion, especially Weyl gravity's fourth-moment terms.
  • MOND external field aext = 0.5 a0
    Extreme external field case for MOND with EFE; the authors note the true value is 0.15a0, so this brackets the prediction.
assumptions (5)
  • domain assumption The galaxy is spherically symmetric and non-rotating, so the Jeans equation (4.1) applies with anisotropy xi=0.
    Used throughout Section IV; departures from sphericity or isotropy would shift the predicted profiles, as the authors acknowledge.
  • domain assumption The baryonic mass distribution is described by the Sersic approximation (2.1).
    Input to all acceleration formulas; adopted from Moffat and Toth's fit to vD18a photometry.
  • domain assumption There is no dark matter in the modeled galaxy.
    The scenario tested; all predictions use baryonic mass only.
  • domain assumption MOG parameter scaling relations (alpha = alpha_inf M/(sqrt(M)+E)^2, mu = D/sqrt(M)) are correct.
    Inherited from Moffat and Toth 2009; determines alpha and mu used for DF2.
  • ad hoc to paper External field effect in MOND can be represented by replacing the interpolating function argument with (a + aext)/a0 and aext = 0.5a0 as an extreme case.
    The authors explicitly call this an extreme case; the true profile lies between isolated MOND and this case, so the quoted chi-square is a bound, not a prediction.

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Cite this review

Pith. "Pith review of Modified Gravity Theories in Light of the Anomalous Velocity Dispersion of NGC1052-DF2." pith.science (2026). https://pith.science/paper/AWN5QOHE

@misc{pith2026190807160,
  author       = {Pith},
  title        = {Pith review of: Modified Gravity Theories in Light of the Anomalous Velocity Dispersion of NGC1052-DF2},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AWN5QOHE}},
  note         = {Machine review of arXiv:1908.07160}
}
abstract

Recent observations of ultra-dwarf galaxy NGC1052-DF2 started an interesting discussion between dark matter hypothesis and modified gravity theories. Reported low velocity dispersion (< 10.5 km/s at 90% confidence level) derived from the kinematic data of 10 globular clusters in the galaxy points towards an extraordinarily low dynamical mass ($\sim$ $3.4 \times 10^{8} M_{\odot}$) which is of the same order of the luminous mass ($\sim$ $2.0 \times 10^{8} M_{\odot}$) in the galaxy. This has been interpreted as the first evidence of a galaxy `without Dark Matter'. It has been argued that dark matter is not necessarily coupled to the the baryonic mass on the galactic scale and poses a challenge to modified gravity theories. We explore the dynamics of NGC1052-DF2 within the context of four popular alternative theories of gravity [Modified Newtonian Dynamcies (MOND), Weyl Conformal gravity, Modified gravity (MOG)/Scalar-Tensor-Vector Gravity (STVG) and Verlinde's Emergent gravity] and present the analysis of detailed radial variation of the velocity dispersion. We demonstrate that the dispersion data of NGC1052-DF2 is fully consistent with modified gravity paradigm (as well as with general relativity without dark matter). We reach similar conclusion for the ultra-dwarf NGC1052-DF4 which has been claimed to be the second candidate for galaxies `without Dark Matter'.

Figures

Figures reproduced from arXiv: 1908.07160 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: The galacto-centric distance to the individual GC is rescaled with D (as different D will yield a different conversion factor between the angular separation and projected radial distances). Though we do not specifically know, whether NGC1052-DF2 is expected to have any…
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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