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REVIEW 3 major objections 6 minor 72 references

Exploring the Dark Matter Disc Model in Dwarf Galaxies: Insights from the LITTLE THINGS Sample

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Dark matter confined to the disc, traced by neutral hydrogen, fits the inner rotation curves of 22 dwarf galaxies as well as the standard halo model while implying 10–100 times less mass.

desk verdict The DMD-vs-NFW comparison is plausible, but the drift correction is model-dependent and the headline mass ratios don't match the table, so the paper needs a serious referee and a revised analysis. read the letter →

arxiv 2412.09934 v1 pith:42AI7Y7G submitted 2024-12-13 astro-ph.GA astro-ph.CO

Francesco Sylos Labini , Roberto Capuzzo-Dolcetta , Giordano De Marzo , Matteo Straccamore This is my paper · ORCID
classification astro-ph.GAastro-ph.CO PACS 95.35.+d98.62.Dm
keywords darkmatterdiscdwarfgalaxiesrotationcurvesLITTLETHINGSasymmetricdriftvelocityringmodelNFWhalocusp-coreproblem
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 asks whether the dark matter around dwarf galaxies lives in a flattened disc that follows the neutral hydrogen gas rather than in the spherical halo assumed by the standard model. Reconstructing the velocity fields of 22 late-type dwarfs from the LITTLE THINGS survey with a new method that separates rotation from radial motions, the authors fit two mass models to the inner rotation curves. They report that a dark matter disc (DMD) model, in which dark matter is traced by the gas and stellar surface densities, matches the data just as well as the standard Navarro-Frenk-White halo, while the total inferred galaxy mass is about ten to a hundred times smaller. If the result holds, dwarf galaxies are much lighter than usually claimed, and the longstanding cusp-core problem would be a geometric effect of where dark matter is located, not a problem that needs feedback from star formation.

What carries the argument

The dark matter disc (DMD) model is the central object: it assumes dark matter in the disc has a surface density equal to gamma_s times the stellar surface density plus gamma_g times the HI gas surface density, with those two weights being the free parameters of the fit. The second load-bearing piece is the velocity ring model (VRM), a flat-disc method that reconstructs coarse-grained two-dimensional maps of the transverse and radial velocity components, which the authors use to decide where the disc is rotationally supported and to build the rotation curves that both mass models must fit. The asymmetric drift correction, derived from the Jeans equations, connects the measured velocity dispersions and the assumed disc density to the circular velocity that the mass models are fit to.

What would settle it

Measure the vertical velocity dispersion or off-plane motions of stars in a face-on dwarf galaxy: a disc-confined dark matter distribution produces a strongly flattened gravitational potential, whereas a spherical halo does not. Alternatively, high-precision gravitational lensing of a background source by a nearby dwarf disc galaxy can map the projected mass distribution directly and would reveal whether the mass is distributed as a disc or a halo.

Watch

Extended reading notes

Core claim

The central claim is that for the 22 dwarf galaxies in the LITTLE THINGS subsample, the dark matter disc model gives statistically comparable fits to the asymmetric-drift-corrected rotation curves as the standard NFW halo model, even though the total mass of the disc (baryons plus disc dark matter) is roughly ten to a hundred times smaller than the NFW virial mass. Within the DMD framework, the paper also establishes that the inner slope of the rotation curve is directly set by the linear combination of the stellar and gas surface density profiles, which have flat cores, so the observed linear rise of the circular velocity with radius in the central regions follows without any additional tuning.

Load-bearing premise

The asymmetric drift correction assumes a particular disc density profile, and in the DMD model that density is built from the same two free parameters the fit is meant to determine, with no iterative or independent scheme given to break the coupling; if the Jeans equation should instead use only the tracer gas density, the DMD rotation curves and masses would be mis-specified.

Editorial extensions

If this is right

  • If the DMD model is correct, the total dynamical masses of dwarf galaxies are 10 to 100 times smaller than estimates based on spherical NFW halos, so baryons dominate the inner mass budget.
  • The cusp-core problem would no longer require feedback or exotic physics to explain flat cores, because a cored disc-like dark matter distribution directly produces linearly rising inner rotation curves.
  • The Bosma effect, the observed correlation between dark matter and HI gas, would be elevated from a phenomenological correlation to a direct structural statement about where dark matter resides.
  • Rotation curve data alone cannot distinguish the two mass models on the scales probed here, so claims of dark matter confinement to discs need independent geometric probes to be settled.
  • Under the DMD model, the inner rotation curve shape is predictable from the observed stellar and gas surface density profiles, providing a built-in cross-check with independent photometric data.

Reading between the lines

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

  • If dark matter is truly confined to galactic discs, standard collisionless cold dark matter would need a dissipative or otherwise self-interacting component that can lose angular momentum and settle into a plane; this is an extension the paper does not make.
  • The same disc hypothesis could be tested in gas-poor dwarf spheroidals by measuring the vertical velocity dispersion of their stars: a flattened mass distribution creates a measurably different vertical potential than a spherical halo.
  • High-precision strong gravitational lensing of a background source by a nearby dwarf disc galaxy would map the projected mass distribution directly and could separate a disc-like from a spherical dark matter geometry.
  • Because the paper's rotation-curve fits only cover a narrow radial range, a concrete follow-up is to ask whether the DMD parameters found here remain stable when the outer, velocity-anisotropic regions are included with a warp treatment.
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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. This paper analyzes the neutral-hydrogen velocity fields of 22 dwarf galaxies from the LITTLE THINGS sample using the velocity ring model (VRM), reconstructs two-dimensional maps of the tangential and radial velocity components, and derives inner-disc rotation curves with an asymmetric-drift correction. The authors fit each rotation curve with two mass models: the standard Navarro-Frenk-White (NFW) halo model and a dark matter disc (DMD) model in which the dark matter surface density is proportional to the stellar and gas surface densities with two free weights γ_s and γ_g. They report that the DMD fits are statistically comparable to the NFW fits and that the DMD masses are 10 to 100 times smaller than the NFW masses. They also argue that the DMD model naturally produces linearly rising inner rotation curves because the baryonic surface densities have cored shapes.

Significance. The paper addresses a question of current interest: whether dwarf galaxy rotation curves can be fitted equally well by a disc-distributed dark matter model and a standard NFW halo. The use of the VRM to map radial and tangential velocity anisotropies in 22 LITTLE THINGS dwarfs is a methodological contribution, and the paper builds on publicly available observations. The explicit formulation of the DMD model in Eqs. (15)-(18) makes the underlying assumption testable. If the comparison were performed self-consistently and the mass-ratio claim were correct, the result would be relevant to the cusp-core problem and to the inferred geometry of dark matter in dwarf galaxies. However, the current manuscript does not provide sufficient evidence for the headline comparison because the DMD drift correction is model-dependent, and the quantitative results in Table 1 contain inconsistencies. The paper does not include machine-checked proofs or released code, so reproducibility rests on the public data and the described procedures.

major comments (3)
  1. [Sections 3.2 and 4, Eqs. (10), (15), (18)] The asymmetric-drift-corrected circular velocity in the DMD case is not an independent observable. The drift correction σ_D^2 in Eq. (10) contains (R/ρ)(∂ρ/∂R), and for the DMD model the authors set ρ ∝ γ_s Σ_s + γ_g Σ_g in Eq. (18). The corrected v_c is therefore a function of the same parameters γ_s and γ_g that the fit in Eq. (15) is meant to determine. The manuscript does not describe an iterative or fixed-point scheme: Section 5 indicates that the DMD surface density is computed 'once the fit with the DMD mass model has been performed,' but the fit uses that surface density to build the data vector that is fitted. For the NFW model, by contrast, ρ in Eq. (10) is the baryonic density (Eq. 17), independent of the NFW parameters, so the two models are not treated symmetrically. This is a load-bearing issue because the fit range is often less than half a decade (Section 6) and several reduced χ² values in Table 1 are below unity, so a small model-induced shift in v_c can substantially change the inferred γ_s and γ_g, and hence M_dmd and the stated mass ratio. The authors should either use a model-independent density (e.g., the baryonic density) in Eq. (10) for both models, or implement and document a fixed-point iteration over γ_s and γ_g with a convergence test.
  2. [Abstract and Table 1] The abstract's claim that the DMD masses are 'approximately 10 to 100 times smaller' than the NFW masses is not supported by the numbers in Table 1. Using the tabulated columns (5) and (6), DDO50 has M200/Mdmd ≈ (0.2×10^10)/(1.8×10^9) ≈ 1.1 and NGC2366 has M200/Mdmd ≈ (1.0×10^10)/(2.8×10^9) ≈ 3.6, while the largest ratios are of order 40 (DDO47, DDO52, DDO101, IC1613) and no listed galaxy reaches a ratio of 100. The abstract and Section 7 should be revised to state the actual range, or the table columns should be corrected.
  3. [Table 1] Table 1 contains several internal inconsistencies between the mass columns and the ratio columns. For DDO101, columns (4) and (6) imply M200/Mbar = (5.5×10^10)/(9.3×10^7) ≈ 591, while column (8) lists 765; for DDO210 the same computation gives ≈222, not 170. The entry for NGC3738, M_dmd = (489±100)×10^9 M⊙, exceeds the listed M200 = (14.6±4)×10^10 M⊙ and is physically implausible for a dwarf galaxy, indicating a unit error or a typo. These issues undermine the quantitative mass comparison and should be fixed before the paper can be properly evaluated.
minor comments (6)
  1. [Section 2] The sentence 'The determination of the inclination angle by Iorio et al. (2017) not always agree with that by Iorio et al. (2017)' should read 'The determination of the inclination angle by Iorio et al. (2017) does not always agree with that by Oh et al. (2015)'.
  2. [Eq. (11)] The sentence contains a doubled 'and' ('the gas and stellar components and and vh(R)'); remove the duplicate.
  3. [Fig. 3 caption] The caption refers to the 'blu line' for the cored profile fit; it should read 'blue line'.
  4. [Throughout] The paper uses 'transversal' where 'tangential' is the standard term in disk kinematics; for consistency with the v_θ notation, consider using 'tangential' throughout.
  5. [Table 1] Columns (9) and (10) are labeled 'χ2_dmd' and 'χ2_nfw', but the text calls these 'reduced χ2' in several places; specify whether the quoted values are reduced and state the number of degrees of freedom used.
  6. [Section 7] The conclusions state that the fits were performed 'to the transversal velocity,' while Section 6 states that they were performed to the asymmetric-drift-corrected circular velocity; make the target of the fit explicit and consistent.

Circularity Check

1 steps flagged · score 6.0 of 10

DMD drift correction puts the fitted γ_s, γ_g into the 'observed' circular velocity (Eqs. 9-10 with Eq. 18), making the DMD data points model-dependent; no iterative scheme is described.

  1. self definitional [Section 3.2 (Eqs. 9-10) coupled with Section 4 (Eq. 18) and Section 6 fitting procedure]
    "In Eqs.9-10 the kinematic terms can be measured from the data while density ρ(R) depends on the mass model adopted as we are going to discuss in the next section. ... For the DMD model, the density of the disc entering the Jeans equation (Eq.2) is given (again, up to an irrelevant prefactor) by ρ(R)∼ Σdmd(R) =γsΣs(R) +γgΣg(R). (18) Specifically, it is a linear combination of the stellar and gas surface densities, rescaled by the two free parameters of the DMD model, γs and γg."

    Inserting Eq.18 into Eq.10 makes σ_D^2, and therefore the 'observed' circular velocity v_c^2 = v_θ^2 + σ_D^2 in Eq.9, depend on the two parameters γs, γg that the fit is supposed to determine from Eq.15. For the NFW model, ρ in Eq.10 is the baryonic density (Eq.17), independent of the NFW parameters, so the DMD and NFW fits are not symmetric: DMD can reshape its own data points while fitting. The paper describes no iterative or fixed-point scheme; Section 6 only says the best-fit parameters minimize χ^2 between the model circular velocity and the observed one. Section 5 then computes Σ_dmd from the fitted γs, γg, fits it to the cored form Eq.19, and feeds it back into Eqs.9-10.

full rationale

The central comparison is partially circular. The paper's own equations show that the DMD circular velocity used as 'data' is built from the same γs, γg that are being fitted, so the statistical comparison with NFW is not on equal footing. Self-citations to prior DMD/VRM papers (Sylos Labini et al. 2023a,b, 2024b) are not the main problem: the current analysis uses public LITTLE THINGS data and re-fits both models, so those citations are supporting context, not load-bearing. The inner-slope consistency argument is a genuine model property rather than a rename. However, because no fixed-point iteration is described, the DMD fits, the χ^2 values, and Mdmd all reduce partly to the fit inputs; the reported mass ratio is additionally a comparison of two model-dependent definitions. The abstract's '10 to 100 times smaller' also does not match the Table 1 ratios, but that is a reporting inconsistency, not circularity. Overall, one substantive self-referential step in the central comparison: score 6.

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

The central results rest on two fitted parameters per galaxy for each mass model, plus auxiliary fits for the velocity dispersion profile and the DMD surface-density profile. The DMD model's defining premise, that dark matter surface density follows the baryonic surface densities with constant weights, is an ad hoc modeling assumption. No new physical entities are introduced.

free parameters (5)
  • gamma_s (DMD stellar scaling) = per galaxy, not tabulated separately; enters M_dmd = gamma_s M_s + gamma_g M_g
    Free parameter of the DMD fit in Eq. 15, scaling the stellar contribution to the disc mass.
  • gamma_g (DMD gas scaling) = per galaxy, not tabulated separately
    Free parameter of the DMD fit in Eq. 15, scaling the gas contribution; for DDO43, DDO46, DDO47, and F564-V3 it is the only fitted parameter because no stellar data are available.
  • NFW r_s and rho_0 = per galaxy, not tabulated separately; M_200 derived from them
    Free parameters of the comparison NFW halo model (Eq. 12), fitted to the same rotation curves.
  • DMD surface-density profile parameters Sigma_0, R_g, beta (Eq. 19) = per galaxy, e.g., beta about 1.9 for CVnIdwA
    Fitted to the model-dependent Sigma_dmd profile and used in the asymmetric drift correction.
  • Sixth-degree polynomial coefficients for sigma(R) = per galaxy
    Polynomial fit to the moment-2 velocity dispersion profile, inserted into Eq. 10 for the asymmetric drift.
assumptions (6)
  • standard math The galaxy is in a steady, axisymmetric state described by the Jeans equations.
    Invoked in Sect. 3.2, Eq. 2.
  • domain assumption Mixed v_R v_z terms are negligible and the mean radial velocity v_R is about zero in the fitted range.
    Stated in Sect. 3.2 when simplifying Eq. 5 to Eq. 9.
  • domain assumption Velocity anisotropies are small enough that sigma_v_theta and sigma_v_R are approximately equal to sigma, with sigma taken from the moment-2 map.
    Stated after Eq. 8 in Sect. 3.2.
  • domain assumption The galactic disc is flat (no warp) over the fitted inner radii.
    Core assumption of the VRM in Sect. 3.1, justified by small orientation-angle variations.
  • ad hoc to paper In the DMD model, dark matter resides in the disc and its surface density is proportional to the stellar and gas surface densities with constant weights gamma_s and gamma_g.
    Model premise in Sect. 4, Eq. 15 and 18, motivated by the Bosma effect.
  • domain assumption The stellar mass-to-light ratio and the 1.4 factor for helium are adopted from Oh et al. (2015).
    Used to convert luminosity profiles to stellar masses and gas masses in Sect. 2.

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Cite this review

Pith. "Pith review of Exploring the Dark Matter Disc Model in Dwarf Galaxies: Insights from the LITTLE THINGS Sample." pith.science (2026). https://pith.science/paper/42AI7Y7G

@misc{pith2026241209934,
  author       = {Pith},
  title        = {Pith review of: Exploring the Dark Matter Disc Model in Dwarf Galaxies: Insights from the LITTLE THINGS Sample},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/42AI7Y7G}},
  note         = {Machine review of arXiv:2412.09934}
}
read the original abstract

We conducted an analysis of the velocity field of dwarf galaxies in the LITTLE THINGS sample, focusing on deriving 2D velocity maps that encompass both the transverse and radial velocity fields. Within the range of radial distances where velocity anisotropies are sufficiently small for the disc to be considered rotationally supported, and where the warped geometry of the disc can be neglected, we reconstructed the rotation curve while taking into account the effect of the asymmetric drift. To fit the rotation curves, we employed the standard halo model and the dark matter disc (DMD) model, which assumes that dark matter is primarily confined to the galactic discs and can be traced by the distribution of \HI{}. Interestingly, our analysis revealed that the fits from the DMD model are statistically comparable to those obtained using the standard halo model, but the inferred masses of the galaxies in the DMD model are approximately 10 to 100 times smaller than the masses inferred in the standard halo model. In the DMD model, the inner slope of the rotation curve is directly related to a linear combination of the surface density profiles of the stellar and gas components, which generally exhibit a flat core. Consequently, the observation of a linear relationship between the rotation curve and the radius in the disc central regions is consistent with the framework of the DMD model.

Figures

Figures reproduced from arXiv: 2412.09934 by the authors.

Figure 1
Figure 1. Illustrative representation of the VRM: the LOS velocity [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. VRM-reconstructed coarse-grained map of the transver [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Profiles of CVnIdwA: (a) total DMD, HI and stellar surface density profiles. The parameters Rg, β of the function in Eq.19 (blu line) are reported in the labels. (b) Velocity dispersion profile σ(R) averaged in rings with a 6th degrees polynomial fit (red line). (c) Orientation angles from the TRM as a function of the radial distance: position angle (upper panel), inclination angle (bottom panel) (a) (b) (c) [PITH_… view at source ↗
Figures from the paper (49 more)
Figure 4
Figure 4. Figure 4: VRM maps of CVnIdwA: (a) transversal velocity component map with resolution [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: VRM maps of CVnIdwA with varying resolution: (a,b,c) transversal velocity component map with resolution [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Residual field map of CVnIdwA withwith resolution [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Best fit with the DMD and NFW models for some of the galaxies in our sample. The circular velocity due to the stellar [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: As Fig.7 but for the remaining galaxies in the sample. [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: Parameters space γs − γg for the THINGS galaxies and the LITTLE THINGS sample [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: The virial mass estimated from the NFW mass model [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]
Figure 11
Figure 11. Figure 11: As Fig.3 but for DDO43 (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]
Figure 12
Figure 12. Figure 12: As Fig.4 but for DDO43 (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]
Figure 13
Figure 13. Figure 13: As Fig.3 but for DDO46. tween the two methods in capturing the overall velocity behav￾ior of the system. Note that in this case we used the inclina￾tion angle i = 27◦ from Oh et al. (2015) which is smaller than that determined by Iorio et al. (2017) (i.e., i = 39◦ ) a…
Figure 14
Figure 14. Figure 14: As Fig.4 but for DDO46. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p018_14.png]
Figure 15
Figure 15. Figure 15: As Fig.3 but for DDO47. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p018_15.png]
Figure 16
Figure 16. Figure 16: As Fig.4 but for DDO47. DDO87 The orientation angles do not exhibit any significant radial trend, indicating that a significant warp is likely not present in this galaxy (see Figures 25-26). However, the velocity maps reveal large angular anisotropies, which align wit…
Figure 17
Figure 17. Figure 17: As Fig.3 but for DDO50 (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p019_17.png]
Figure 18
Figure 18. Figure 18: As Fig.4 but for DDO50. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p019_18.png]
Figure 19
Figure 19. Figure 19: As Fig.3 but for DDO52. NFW and DMD models fit the data equally well, with reduced χ 2 values of 2.5 and 1.4, respectively. DDO126 Similar to DDO101, DDO126 also exhibits a regular LOS ve￾locity map. The P.A. shows a variation in the inner disc and remains constant as…
Figure 20
Figure 20. Figure 20: As Fig.4 but for DDO52. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p020_20.png]
Figure 21
Figure 21. Figure 21: As Fig.3 but for DDO53 (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p020_21.png]
Figure 22
Figure 22. Figure 22: As Fig.4 but for DDO53 veal significant and localized anisotropies both in the inner and outer regions of the disc. These anisotropies indicate variations in the velocity components in different directions, occurring in specific regions of the galaxy. Even in this cas…
Figure 23
Figure 23. Figure 23: As Fig.3 but for DDO70 (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p021_23.png]
Figure 24
Figure 24. Figure 24: As Fig.4 but for DDO70 (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p021_24.png]
Figure 25
Figure 25. Figure 25: As Fig.3 but for DDO87 results in terms of the reduced χ 2 , i.e., ∼ 1.5, with the relatively large value being attributed to the outermost data points. DDO168 DDO168 exhibits a regular LOS velocity map in the inner part of its disc, with an almost aligned kinematic a…
Figure 26
Figure 26. Figure 26: As Fig.4 but for DDO87. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p022_26.png]
Figure 27
Figure 27. Figure 27: As Fig.3 but for DDO101. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p022_27.png]
Figure 28
Figure 28. Figure 28: As Fig.4 but for DDO101. DDO210 In the case of DDO210, the LOS velocity anisotropy field ap￾pears irregular, as depicted in Figures 37 and 38. The orien￾tation angles do not exhibit a radial trend, suggesting that the assumption of a flat disc made by the VRM is a goo…
Figure 29
Figure 29. Figure 29: As Fig.3 but for DDO126. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p023_29.png]
Figure 30
Figure 30. Figure 30: As Fig.4 but for DDO126. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p023_30.png]
Figure 31
Figure 31. Figure 31: As Fig.3 but for DDO133. which are larger toward the outskirts of the galaxy. These outer regions, where a warp may possibile be present, are not in￾cluded in the fits for the mass models. The fits with both mass models are comparable and are clearly influenced by the…
Figure 32
Figure 32. Figure 32: As Fig.4 but for DDO133. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p024_32.png]
Figure 33
Figure 33. Figure 33: As Fig.3 but for DDO154. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p024_33.png]
Figure 34
Figure 34. Figure 34: As Fig.4 but for DDO154. In the inner part of the disc, the rotation curve is compara￾tively more regular but remains affected by considerable fluc￾tuations. Moreover, discrepancies arise between the measure￾ments obtained using the TRM and the VRM, primarily due to t…
Figure 35
Figure 35. Figure 35: As Fig.3 but for DDO168. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p025_35.png]
Figure 36
Figure 36. Figure 36: As Fig.4 but for DDO168. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p025_36.png]
Figure 37
Figure 37. Figure 37: As Fig.3 but for DDO210. results for the rotation velocity. The two mass models provide similarly good fits to the data, with a reduced χ 2 of 0.92. NGC3738 NGC3738 exhibits an irregular shape and a LOS velocity field characterized by irregular and asymmetrical patter…
Figure 38
Figure 38. Figure 38: As Fig.4 but for DDO210. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p026_38.png]
Figure 39
Figure 39. Figure 39: As Fig.3 but for DDO216. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p026_39.png]
Figure 40
Figure 40. Figure 40: As Fig.4 but for DDO216. anisotropies in the outermost regions. Both mass models pro￾vide a reasonable fit to the data, with comparable χ 2 values [PITH_FULL_IMAGE:figures/full_fig_p026_40.png]
Figure 41
Figure 41. Figure 41: As Fig.3 but for F564-V3. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p027_41.png]
Figure 42
Figure 42. Figure 42: As Fig.4 but for F564-V3. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p027_42.png]
Figure 43
Figure 43. Figure 43: As Fig.3 but for IC10. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p027_43.png]
Figure 44
Figure 44. Figure 44: As Fig.4 but for IC10 [PITH_FULL_IMAGE:figures/full_fig_p027_44.png]
Figure 45
Figure 45. Figure 45: As Fig.3 but for IC1613. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p028_45.png]
Figure 46
Figure 46. Figure 46: As Fig.4 but for IC1613. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p028_46.png]
Figure 47
Figure 47. Figure 47: As Fig.3 but for NGC2366. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p028_47.png]
Figure 48
Figure 48. Figure 48: As Fig.4 but for NGC2366 [PITH_FULL_IMAGE:figures/full_fig_p028_48.png]
Figure 49
Figure 49. Figure 49: As Fig.3 but for NGC3738. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p029_49.png]
Figure 50
Figure 50. Figure 50: As Fig.4 but for NGC3738. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p029_50.png]
Figure 51
Figure 51. Figure 51: As Fig.3 but for WLM. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p029_51.png]
Figure 52
Figure 52. Figure 52: As Fig.4 but for WLM [PITH_FULL_IMAGE:figures/full_fig_p029_52.png]

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72 extracted references · 67 canonical work pages

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.