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Exploring velocity dispersion anisotropy in a dark matter dominated ultra-diffuse galaxy with modified gravity models

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper claims that MOND and RGGR can match the line-of-sight velocity dispersion of the dark-matter-dominated ultra-diffuse galaxy DF44 as well as an NFW dark matter halo does, once orbital anisotropy is allowed; a generic f(R) model…

desk verdict A solid, honest fitting study that adds anisotropy to the DF44 modified-gravity comparison; the MOND/RGGR competitiveness claim is real but conditional on ignoring the Coma external field, which prior work found fatal for MOND. read the letter →

arxiv 2412.03658 v1 pith:AHFXDMWO submitted 2024-12-04 astro-ph.CO astro-ph.GA

Esha Bhatia , Sayan Chakrabarti , Sovan Chakraborty This is my paper · ORCID
classification astro-ph.COastro-ph.GA
keywords ultra-diffusegalaxiesNGC1052-DF44line-of-sightvelocitydispersionorbitalanisotropymodifiedNewtoniandynamics(MOND)f(R)gravityRGGRrunninggravitationalconstantNFWdarkmatterhalo
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

NGC1052-DF44 is an ultra-diffuse galaxy, a large but very faint galaxy, whose stellar motions are so fast that ordinary stars alone cannot bind it; this is usually read as a dark matter signal. The paper asks whether three gravity models that avoid dark matter can produce the same observed line-of-sight velocity dispersion. It concludes that MOND and RGGR fit the data as well as the standard cuspy NFW dark matter halo profile does, while a generic f(R) model fits but is statistically less competitive. It also finds that allowing the stellar orbits to have a constant tangential anisotropy fits as well as the common isotropic assumption in all models. If this result holds, DF44 does not cleanly discriminate dark matter from modified gravity, and orbital anisotropy is a necessary part of such tests.

What carries the argument

The load-bearing machinery is the spherical Jeans equation, converted into a fast analytic integral for the projected line-of-sight velocity dispersion $\sigma_{\rm LOS}^2(r)$ with a kernel $K$ that encodes the anisotropy parameter $\xi$: zero for isotropic motion, a fitted constant for the tangential/radial case, and the Osipkov-Merritt scale radius for the radial profile. The modified gravity models enter through an effective mass function in that integral: MOND through its interpolation function and the fixed acceleration scale $a_0$, $f(R)$ through a Yukawa correction to the Newtonian potential with coupling $\delta$ and scale $\lambda$, and RGGR through the running of $G$ represented by the parameter $\bar\nu$. The stellar mass is a de-projected Sersic profile scaled by a fitted mass-to-light ratio $\gamma_*$, and the parameters are scanned with a Markov chain Monte Carlo sampler and ranked with the Bayesian information criterion.

What would settle it

Recompute the best-fit MOND and RGGR models with the Coma cluster external field included; if the predicted line-of-sight velocity dispersion at 5.1 kpc falls below the observed about 41 km/s, as the earlier external-field MOND calculation quoted in the paper found, the competitive-fit claim fails. A complementary check is DF44's three-dimensional position and velocity relative to Coma: if the galaxy is not on a first infall, the proposed suppression of the external field cannot rescue the isolated fits.

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Extended reading notes

Core claim

The paper's central claim is that, in an isolated, spherically symmetric Jeans treatment of NGC1052-DF44, dark matter is not uniquely required: MOND with its fixed acceleration scale ($a_0 = 1.14 \times 10^{-8}\,\text{cm/s}^2$) and RGGR with a slowly running gravitational coupling ($\bar\nu \approx 2.5 \times 10^{-8}$) both reproduce the observed line-of-sight velocity dispersion as well as the standard cuspy NFW dark matter halo does ($\chi^2_{\rm red} = 0.39$ and $0.45$ versus $0.75$). A generic $f(R)$ model with a Yukawa correction also fits the data, but its Bayesian information criterion is worse than that of NFW, so the authors count it as not competitive. In every model, a constant tangential orbital anisotropy fits as well as, or slightly better than, the usual isotropic assumption, while the radially dependent Osipkov-Merritt profile is strongly disfavored. The conclusion is that, with anisotropy allowed, DF44 does not separate dark matter from modified gravity.

Load-bearing premise

The gravity-model fits assume DF44 is isolated, so they leave out the external gravitational field of the Coma cluster in which the galaxy sits; if that external field acts on the galaxy in the usual way, the MOND and RGGR fits lose their physical basis.

Editorial extensions

If this is right

  • MOND and RGGR each match the observed line-of-sight velocity dispersion of DF44 without a dark matter component, so this ultra-diffuse galaxy is not a decisive dark matter detection once modified gravity is allowed.
  • A constant negative (tangentially biased) anisotropy fits as well as isotropy in every model tested, so velocity-dispersion data alone cannot fix both the gravity law and the orbital structure.
  • The Osipkov-Merritt radial anisotropy profile is strongly disfavored by Bayesian information criterion in all three gravity models, ruling out a simple radial-orbit alternative for DF44.
  • The generic f(R) model fits the data but is statistically less competitive than NFW, so this particular Yukawa-type modification is constrained by DF44.
  • The inferred mass-to-light ratio shifts when anisotropy is introduced, so stellar masses and dark matter fractions derived from isotropic Jeans modeling carry a systematic uncertainty.

Reading between the lines

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

  • If the same anisotropy-gravity degeneracy holds for other ultra-diffuse galaxies, re-fitting existing isotropic velocity-dispersion datasets with a constant anisotropy parameter is a direct test of how much of the reported dark matter signal is actually orbital structure.
  • The external-field issue that already undermines the Coma MOND fit applies in principle to the RGGR and f(R) fits here; recomputing both models with the Coma cluster's gravitational field included would show whether their competitiveness survives.
  • Because MOND and RGGR scale differently with acceleration and gravitational potential energy, a sample of ultra-diffuse galaxies at different masses and cluster-centric distances could separate the two models, something one galaxy cannot do.
  • The fits prefer tangentially biased globular-cluster orbits, a preference that is in principle checkable with tangential proper motions or higher-order velocity moments.
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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 / 4 minor

Summary. The paper performs a kinematic analysis of the ultra-diffuse galaxy NGC1052-DF44 under four dynamical models: a Navarro-Frenk-White (NFW) dark matter halo, MOND, a generic Yukawa-like f(R) gravity, and RGGR. For each model, the line-of-sight velocity dispersion is computed with the Jeans equation under three anisotropy prescriptions (isotropic, constant, and Osipkov-Merritt), with parameters constrained by MCMC and models compared by BIC. The central findings are that all three gravity models can fit the observed velocity dispersion in at least one anisotropy scenario, that MOND and RGGR are statistically competitive with NFW while f(R) is less favored, and that constant tangential anisotropy is competitive with isotropy while the Osipkov-Merritt profile is strongly disfavored.

Significance. If the central claim holds, the paper would provide a useful systematic comparison of modified-gravity models against dark-matter halos in a single well-studied UDG, extending earlier isotropic analyses to anisotropic velocity dispersion. The paper's strengths are the use of a common anisotropic Jeans framework, the simultaneous treatment of three gravity models and an NFW halo, and the use of BIC rather than only chi-squared for model comparison. However, the headline 'competitive' claim is conditional on an isolated-galaxy approximation that is explicitly acknowledged but not tested, and the statistical reporting is incomplete (no parameter uncertainties, no stated number of data points, and a non-standard BIC penalty). These issues currently limit the strength of the conclusions.

major comments (4)
  1. [Sec. III A, III C, VI] The central claim that MOND and RGGR are competitive with NFW rests on the isolated-galaxy approximation. Equation (13) for MOND and Eq. (19) for RGGR use only the internal Newtonian potential of the galaxy, and Sec. VI states 'we avoid the complications of EFE.' However, DF44 is embedded in the Coma cluster, and reference [36] (cited in the introduction) found that including the Coma external field in MOND fails to reproduce the observed velocity dispersion, with only a non-equilibrium infall scenario [41] as a possible rescue that is not modeled here. The abstract's statement that 'only MOND and RGGR remain competitive with NFW DM' is therefore not a physical MOND/RGGR prediction for DF44 unless the external field is effectively suppressed. The paper should either include an EFE-inclusive analysis (at least for MOND, where the framework is available) or explicitly and prominently qualify the headline conclusion to the isolated approximation.
  2. [Sec. V C] The text states that the authors 'probe the kinematics for two RGGR frameworks, i.e., an isolated scenario and under the influence of external effects, as discussed below,' but only the isolated scenario is presented. No external-field RGGR model or associated results appear in the paper. This promised analysis is directly relevant to the EFE concern raised in the previous comment; the paper should either provide the external-field RGGR results or remove the claim that two frameworks are studied.
  3. [Eq. (21), Tables I-IV] The BIC formula as written is non-standard: BIC = -2 log L + 2k log(n) differs from the Schwarz criterion, BIC = -2 log L + k log N. The number of data points N (called n in Eq. (21)) is never given anywhere in the paper. Since the BIC differences and the interpretation thresholds in Sec. IV (e.g., ΔBIC < 2, 2-6, >6) depend on the penalty term, the model-comparison results in Tables I-IV cannot be verified as presented. Please correct the formula, define and report N, and recompute the BIC values and thresholds accordingly.
  4. [Tables I-III] The best-fit parameters are reported without any uncertainties, despite the use of an MCMC sampler. Without posterior intervals (e.g., 16th-84th percentiles), it is impossible to assess whether the parameters are well constrained, which is especially important for the f(R) parameters that lie close to the prior boundary (e.g., δ = -0.90 in Table II) and for the 'inconclusive' ΔBIC differences of about 2 between isotropic and constant anisotropy. Please report parameter uncertainties and state the priors and their boundaries explicitly.
minor comments (4)
  1. [Sec. II, Fig. 1] The text refers to a 'green dashed line' for the NFW case, but Fig. 1 and its caption show a green solid line; please correct the inconsistency.
  2. [Throughout] The anisotropy profile is repeatedly called 'Osikpov-Merritt'; the correct spelling is 'Osipkov-Merritt' (also in the figure captions and tables).
  3. [Eqs. (1), (3), (4)] Several equations in Sec. II appear to have lost the radial coordinate symbol in the typeset version (e.g., the density argument in Eq. (1) and the mass integral in Eq. (3)). Please ensure all radial variables are shown consistently.
  4. [Sec. IV] The BIC interpretation thresholds (ΔBIC < 2, 2-6, >6) are stated without a specific citation; please add a reference, and ensure the thresholds are consistent with the corrected BIC definition.
Assumptions & free parameters 15 free parameters · 8 assumptions · 0 invented entities

The central comparison rests on multiple fitted parameters per model: the stellar mass-to-light ratio, the anisotropy parameters, and the gravity-model parameters (delta and lambda for f(R), nu_bar for RGGR, M200 for NFW). These are tuned to the same velocity dispersion data used to declare the models competitive. The axioms are the standard Jeans machinery plus the specific weak-field forms of MOND, f(R), and RGGR, and the isolation assumption that excludes the Coma cluster external field.

free parameters (15)
  • MOND gamma* = 1.02 (isotropic), 1.31 (constant), 1.00 (OM)
    Stellar mass-to-light ratio fitted to the observed velocity dispersion.
  • MOND constant anisotropy xi = -0.41
    Anisotropy parameter fitted in the constant anisotropy model.
  • MOND Osipkov-Merritt radius ra = 5.67 kpc
    Scale radius of the radially varying anisotropy profile.
  • f(R) gamma* = 1.56 (isotropic), 1.83 (constant), 2.49 (OM)
    Stellar mass-to-light ratio fitted to the same data.
  • f(R) coupling delta = -0.89, -0.90, -0.81
    Yukawa coupling fitted for each anisotropy model; values sit at the edge of the allowed (-1,0) range.
  • f(R) scale length lambda = 0.81, 2.46, 3.49 kpc
    Yukawa scale length fitted to the galaxy size.
  • f(R) constant anisotropy xi = -0.17
    Anisotropy parameter fitted in the constant anisotropy model.
  • f(R) Osipkov-Merritt radius ra = 4.39 kpc
    Scale radius of the radially varying anisotropy profile.
  • RGGR gamma* = 1.45, 1.59, 1.44
    Stellar mass-to-light ratio fitted in the three anisotropy scenarios.
  • RGGR nu_bar = 2.46e-8, 2.75e-8, 1.79e-8
    Running-G phenomenological parameter fitted to the velocity dispersion.
  • RGGR constant anisotropy xi = -0.34
    Anisotropy parameter fitted in the constant anisotropy model.
  • RGGR Osipkov-Merritt radius ra = 5.56 kpc
    Scale radius of the radially varying anisotropy profile.
  • NFW M200 = 3.98e10 M_sun (text); 0.70e11 M_sun (Fig.1 caption)
    Virial mass fitted for the dark matter comparison model; caption and text disagree.
  • NFW constant anisotropy xi = -0.8
    Anisotropy parameter fitted in the dark matter comparison.
  • NFW gamma* = not reported
    Mass-to-light ratio is stated to be a free parameter but its best-fit value is not given.
assumptions (8)
  • domain assumption Spherical Jeans equation with steady-state equilibrium.
    Eq.(1) in Section II models the galaxy as a spherical, collisionless system in dynamical equilibrium.
  • domain assumption Mamon-Lokas projection formula applies to modified gravity via an effective enclosed mass.
    Eq.(5) uses the reduced kernel expression; replacing modified-force accelerations by an effective mass is approximate for non-Newtonian potentials.
  • domain assumption Sersic profile parameters for DF44 are n=0.94, r_eff=4.7 kpc, L_tot=2.33e8 L_sun at 100 Mpc.
    Taken from van Dokkum et al. [24] and used in Eq.(6) for the luminosity density.
  • domain assumption f(R) weak-field Yukawa potential of Eq.(15) follows from a Taylor expansion about R=0.
    Section III.B assumes the expansion and the resulting potential without re-deriving its validity on galactic scales.
  • domain assumption RGGR beta function Eq.(16) and potential-energy relation Eq.(18).
    Taken from prior RGGR literature [45,46,59,60]; not derived in this paper.
  • domain assumption Isolation: the Coma cluster external field is neglected.
    Stated explicitly in the conclusion as avoiding EFE; [36] found the MOND EFE fails for DF44.
  • domain assumption NFW concentration parameter is fixed by the c-M200 relation.
    In the NFW fit, c is set using Diemer and Kravtsov [54], leaving M200 as the fitted dark matter parameter.
  • domain assumption MOND interpolating function mu(x)=x/sqrt(1+x^2).
    Assumed in Eq.(12) without fitting or testing alternate interpolating functions.

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Pith. "Pith review of Exploring velocity dispersion anisotropy in a dark matter dominated ultra-diffuse galaxy with modified gravity models." pith.science (2026). https://pith.science/paper/AHFXDMWO

@misc{pith2026241203658,
  author       = {Pith},
  title        = {Pith review of: Exploring velocity dispersion anisotropy in a dark matter dominated ultra-diffuse galaxy with modified gravity models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AHFXDMWO}},
  note         = {Machine review of arXiv:2412.03658}
}
abstract

The kinematics of the ultra-diffuse galaxy (UDG) NGC1052-DF44 is primarily influenced by the presence of dark matter (DM). In this paper, we conduct a contrasting kinematic study of DF44 within the alternative modified gravity framework. In comparison to NFW DM, we test three alternative gravity models viz Milgromian dynamics (MOND), characterized by a known acceleration scale, a generic $f(R)$ model, assuming an expansion of the Ricci scalar, and a quantum gravity-inspired Renormalization Group correction to General Relativity (RGGR), which involves the running of the gravitational coupling parameter $G$ with the Universe's energy scale. For each gravity model, we evaluate the velocity dispersion (VD) of the galaxy beyond the conventional radial isotropic assumption and extend to two anisotropy scenarios, i.e., constant and Osipkov-Merritt. Our results show that all three gravity models can provide consistent fits to the observed VD of DF44; however, only MOND and RGGR remain competitive with NFW DM. Interestingly, the constant anisotropy scenario in all the models is also found to be competitive with the complete isotropic assumption.

Figures

Figures reproduced from arXiv: 2412.03658 by the authors.

Figure 1
Figure 1. FIG. 1. The VD for DF44 when the underlying gravity is Newtonian or with an NFW DM halo. The plot represents [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The analytical VD radial profile assumes that the underlying gravity is MOND. The dashed black line shows the VD [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The radial VD variation for DF44 galaxy under the assumption that the underlying gravity is [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The radial VD obtained for DF44 when the underlying gravity is RGGR. The plot shows the VD modeling for three [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The radial Osikpov-Merritt profile for three modified gravity models. The blue dotted line depicts the anisotropy [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The plot compares the three alternative gravity and NFW DM models for the constant anisotropic case. The blue [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

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  1. Exploring Non-minimal coupling using ultra-diffuse galaxies

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