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REVIEW 3 major objections 5 minor 58 references

Testing dark matter density profiles based on Pad\'e approximants of different orders

T0 review · 3 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read The paper claims that low-order Padé rational functions can serve as empirical density profiles for dark matter halos, fitting rotation curves as well as standard models in most galaxies and dramatically outperforming them in one, U11748.

desk verdict A modest, honest empirical paper: the new Padé profiles are a workable addition to the halo-fitting toolbox, but the one striking success (U11748) is also where the untested halo-only assumption does the most work. read the letter →

arxiv 2607.20262 v1 pith:DEUJJLKU submitted 2026-07-22 astro-ph.GA

Talgar Konysbayev , Orlando Luongo , Marco Muccino , Yergali Kurmanov , Kuantay Boshkayev , Gulnara Suliyeva , Ainur Urazalina , Guldana Rabigulova This is my paper
classification astro-ph.GA
keywords darkmatterhalosrotationcurvesPadéapproximantsdensityprofilesBayesianinformationcriteriongalaxydynamicsphenomenologicalmodelsMCMC
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 authors ask whether simple rational functions—specifically Padé approximants—can be used as empirical density profiles for dark matter halos. They define three low-order Padé profiles, fit them to the rotation curves of eight galaxies, and compare them with six conventional halo models using the Bayesian Information Criterion. They find the Padé profiles are generally viable: they fit comparably to standard models in most galaxies, often degenerating into an isothermal-like form when data are sparse, and in one galaxy (U11748) the Padé 03 profile is strongly preferred over every standard model (ΔBIC > 60). The aim is to provide a flexible, parameter-light phenomenological tool for reconstructing rotation curves and estimating halo masses, not to propose a fundamental dark matter model.

What carries the argument

The central object is the Padé approximant, a ratio of two polynomials used as a density law. Three profiles are tested: Padé 02, ρ = ρ0/(1+b1 x+b2 x^2); Padé 12, ρ = ρ0(1+a1 x)/(1+b1 x+b2 x^2); and Padé 03, ρ = ρ0/(1+b1 x+b2 x^2+b3 x^3), with x = r/r0. The condition ρ(r0) = ρ0/2 reduces the number of free parameters, and the rational form lets the profile adjust both inner slope and outer falloff without a fixed asymptotic behavior. Mass functions are computed analytically for the 02 and 12 profiles and numerically for the 03 profile; fits are performed with Metropolis-Hastings MCMC under positivity and pole-free constraints.

What would settle it

Re-fit U11748's rotation curve with an explicit baryonic disk, gas, and bulge included; if a standard model then achieves a lower BIC than the halo-only Padé 03 fit, the paper's central claim—that the rational profile best describes that galaxy's dark-matter distribution—would be falsified.

Watch

Extended reading notes

Core claim

Low-order Padé rational functions—ratios of polynomials used as density laws—can reconstruct galaxy rotation curves phenomenologically. The Padé 03 profile, whose density falls as x^{-3} at large radius, gives the best fit (ΔBIC = 0) for U11748, the one galaxy whose rotation curve clearly flattens at large radii; all six conventional two-parameter profiles are strongly excluded for that galaxy (ΔBIC > 60). For the other seven galaxies the Padé profiles perform comparably but are generally not preferred; the Padé 02 coefficients often approach b1 ≈ 0 and b2 ≈ 1, making it degenerate with the pseudo-isothermal profile. The paper concludes that the rational construction is a useful empirical to

Load-bearing premise

The analysis assumes each rotation curve is produced entirely by a spherical dark-matter halo, with stellar disk, gas, and bulge contributions neglected; if baryons contribute non-negligibly, the inferred density profiles, halo masses, and model rankings change.

Editorial extensions

If this is right

  • The Padé profiles provide a parameter-efficient check for whether a rotation curve contains more radial structure than simple two-parameter halo models can capture.
  • For galaxies with extended flat rotation curves, higher-order Padé profiles may be systematically preferred; for truncated or low-quality data the extra coefficients will be weakly constrained and penalized by the BIC.
  • Halo masses inferred from Padé fits are broadly consistent with those from standard profiles, supporting their use as an empirical mass estimator.
  • The tendency of Padé 02 to degenerate into the pseudo-isothermal profile explains why low-order rational models are often competitive with cored halo models.

Reading between the lines

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

  • Applied to simulated halos with known density profiles, the same Padé family could reveal how many coefficients are needed to recover a given input profile, clarifying how much physical information the rational form actually carries.
  • Because the Padé profiles are not tied to a fixed asymptotic behavior, they may be useful as smooth interpolants for non-parametric density reconstructions from other tracers, such as gravitational lensing or stellar kinematics.
  • If the fitted Padé coefficients correlate with halo concentration or formation history, the family could become a universal rotation-curve parametrization in the spirit of the Persic–Salucci–Stel universal curve, which the authors mention as future work.
  • A natural test: apply the Padé profiles to galaxies with both extended Hi rotation curves and independent mass measurements (e.g., from lensing); if the Padé-derived densities disagree with independent reconstructions, the empirical nature of the claim is exposed.
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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 / 5 minor

Summary. The paper introduces three rational ('Padé-inspired') density profiles — ρ02, ρ12, and ρ03 — as empirical descriptions of dark matter halos, and fits them to published rotation curves of eight galaxies (four ESO and four UGC galaxies). The analysis assumes the rotation curves are dominated by a spherical dark-matter halo (Eq. 4), estimates parameters with a Metropolis–Hastings MCMC, and compares models via the Bayesian Information Criterion. The main conclusion is that the Padé profiles are competitive but generally not preferred over standard two-parameter profiles, with one striking exception: for U11748, Padé 03 reportedly gives the lowest BIC and standard models are strongly disfavored. The paper explicitly frames the profiles as phenomenological and acknowledges the halo-only assumption as a limitation.

Significance. If the analysis were sound, the paper would provide a flexible, closed-form rational family for empirical rotation-curve reconstruction, capable of interpolating between cored and cusped behaviors without committing to a specific asymptotic form. The BIC-based comparison is an appropriate tool for the stated goal, and the paper is transparent about its assumptions and scope. However, several load-bearing technical issues — a prior inconsistency in the U11748 table, an untested halo-only assumption that is decisive for the paper's strongest claim, and an incorrect numerical statement about ΔBIC — currently prevent the results from being fully reproducible or the central claim from being supported as written.

major comments (3)
  1. [Eq. (16a) and Table VIII] The stated uniform prior is ρ0 ∈ [0,1000]×10^-3 M⊙ pc^-3, i.e. an upper bound of 1 M⊙ pc^-3. The reported ISO best fit for U11748 in Table VIII is ρ0 = 47314.21 × 10^-3 M⊙ pc^-3 ≈ 47 M⊙ pc^-3, which exceeds the prior by a factor of ~47. As written, the MCMC cannot produce this point, so either the prior, the table entry, or the units are misreported. This directly affects the BIC comparison for U11748 and must be corrected.
  2. [Eq. (4), Sec. III, Sec. IV.B (U11748)] The analysis assumes v_tot^2 ≈ v_halo^2 throughout, as stated in Eq. (4). This assumption is load-bearing for the paper's strongest specific result: the claim that Padé 03 is strongly preferred for U11748 assumes the entire observed RC is due to a spherical DM halo. If baryonic disk/gas contributes to the inner rise or outer flattening, the extra flexibility of Padé 03 could be fitting the total mass distribution and the BIC ranking could change. No baryonic decomposition or robustness test is provided. The conclusion that the Padé profiles 'appear plausible in explaining the dark matter nature' is therefore not supported for the decisive case; please either add a baryonic-component model or an explicit sensitivity test, or restrict the claim to empirical RC reconstruction.
  3. [Sec. IV.B and Table VIII] The text states that for U11748 'All the other models are strongly excluded (ΔBIC>60)'. Table VIII gives ΔBIC values of 26 (Beta), 36 (Brownstein), 21 (Burkert), 134 (Exp. Sphere), 41 (ISO), and 32 (Persic). Thus the claim ΔBIC>60 is incorrect for five of the six standard models. While strong exclusion remains true (all ΔBIC > 10), the specific numerical claim in the central result must be corrected to match the table.
minor comments (5)
  1. [Sec. IV.B and Sec. IV.C] The text refers to 'Padé 20', 'Padé 21', and 'Padé 30' in the discussion of U11454 and in Sec. IV.C. The paper defines only Padé 02, Padé 12, and Padé 03. These appear to be typos and should be corrected to avoid confusion.
  2. [Fig. 1 caption] Fig. 1 shows the standard phenomenological profiles (Beta, Brownstein, Burkert, Exponential Sphere, Isothermal, Persic), but the caption says 'fitted using the new phenomenological DM models'. This is likely a remnant of an earlier draft; the caption should describe the standard models.
  3. [Table VIII] Arithmetic inconsistency: for U11748, BIC_min is 21 (Padé 03), Padé 02 has BIC=25, so ΔBIC should be 4, not 3 as listed. The Padé 12 entry (BIC=24, ΔBIC=3) is correct.
  4. [Sec. III (data description)] The paper does not provide the number of data points N per galaxy. Since BIC depends on N, this is needed to reproduce the listed BIC values. Also, the source of the RC data (beyond references to earlier work) should be given explicitly, for example by citing the original data papers or providing a table with the data.
  5. [Sec. II.B] The profiles are called 'Padé-inspired', but they are not Padé approximants of a known series or function. This is fine scientifically, but the terminology in the title and abstract might overstate the connection. Consider clarifying that these are rational functions motivated by Padé forms, not approximants to a specific expansion.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the Padé profiles are empirical fits judged by BIC, not predictions derived from their own inputs.

full rationale

The paper's derivation chain is a model-comparison exercise. Three Padé rational density laws are posited (Eqs. 3a–3c), the observed rotation curve is approximated as purely halo-driven (Eq. 4), parameters are inferred by MCMC, and model performance is ranked by BIC (Eqs. 18–19). There is no step in which an output is defined in terms of an input or in which a fitted quantity is relabeled as a prediction. The BIC differences reported in Tables II–IX are direct fit statistics, and the authors explicitly present the Padé profiles as empirical fitting functions rather than as predictions derived from first principles. The main limitation—the neglect of baryonic contributions in Eq. (4)—is an assumption about the data-model link, not a circular reduction; it does not make the fitted profile equal to the observed data by construction. Self-citations (e.g., Refs. [35–39] for mass functions of standard profiles) are used only for standard integrals and do not carry the central claim; no uniqueness theorem or prior ansatz is imported to force the Padé choice. The post-hoc prominence of U11748 is a selection/discussion issue, not circularity. The analysis is self-contained as a phenomenological fitting study and is openly compared against external standard profiles and observed data.

Assumptions & free parameters 5 free parameters · 6 assumptions · 1 invented entities

The central claim rests on a small set of fitted rational functions plus a set of modeling conventions: spherical symmetry, halo-only dynamics, a normalization condition, and chosen priors. The Padé coefficients are fitted, not predicted, and the paper's conclusion is correspondingly framed as phenomenological.

free parameters (5)
  • ρ0 (central density scale) = per galaxy, Tables II-IX
    Fitted to each rotation curve for all profiles, including the Padé models.
  • r0 (scale radius) = per galaxy, Tables II-IX
    Fitted scale radius; defined through the normalization condition ρ(r0)=ρ0/2 in Eq. (11).
  • a1 (Padé 12 numerator coefficient) = per galaxy, Table II-IX entries for Padé 12
    Free parameter in Eq. (3b); controls the x^{-1} outer behavior of Padé 12.
  • b1 (Padé denominator coefficient) = per galaxy, Tables II-IX
    Free parameter in all three Padé profiles; fitted to the rotation-curve shape.
  • b2 (Padé denominator coefficient) = Padé 03 fitted per galaxy; Padé 02/12 derived via Eqs. (12)-(13)
    Independent only for Padé 03; for Padé 02 and Padé 12 it is fixed by the ρ(r0)=ρ0/2 normalization.
assumptions (6)
  • domain assumption Spherical halo-only approximation: v_tot^2 ≈ v_halo^2 (Eq. 4).
    Baryonic disk, gas, and bulge contributions are neglected; all inferred densities are treated as dark matter.
  • domain assumption The eight selected galaxies have rotation curves dominated by dark matter.
    Stated in the abstract and Sec. III; no baryonic decomposition is provided to support the assumption.
  • ad hoc to paper Normalization condition ρ(r0)=ρ0/2 (Eq. 11).
    Imposed to reduce parameter degeneracy and give r0 a common meaning; it is a convention, not derived from physics or data.
  • domain assumption Uniform priors: ρ0∈[0,1000]×10^-3 M⊙/pc^3, r0∈[0,20] kpc, coefficients in [-10,10] (Eqs. 16-17).
    Prior ranges can influence posteriors, especially for weakly constrained Padé coefficients.
  • standard math Gaussian independent errors in the likelihood (Eq. 15).
    Standard assumption for RC fitting; the observed errors are treated as known and independent.
  • ad hoc to paper Padé profiles are used only over the radial range covered by data.
    Padé 12 has an unphysical outer behavior (ρ ∼ x^{-1}); the paper restricts use to the fitted interval, which limits physical extrapolation.
invented entities (1)
  • Padé-inspired rational density profiles (ρ02, ρ12, ρ03)
    purpose: Empirical fitting functions for dark-matter halo density from galaxy rotation curves.
    Introduced in Eqs. (3a)-(3c); not derived from a microscopic dark-matter model, N-body simulations, or an independent observable. Their only support is the fit to the same rotation curves used to determine their coefficients.

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Pith. "Pith review of Testing dark matter density profiles based on Pad\'e approximants of different orders." pith.science (2026). https://pith.science/paper/DEUJJLKU

@misc{pith2026260720262,
  author       = {Pith},
  title        = {Pith review of: Testing dark matter density profiles based on Pad\'e approximants of different orders},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DEUJJLKU}},
  note         = {Machine review of arXiv:2607.20262}
}
read the original abstract

We investigate whether low-order Pad\'e rational functions can be used as empirical density profiles for modeling dark matter halos from galaxy RCs. We introduce three parameterizations determined from Pad\'e series, denoted Pad\'e 02, Pad\'e 12 and Pad\'e 03, and compare them with pseudo-isothermal, Burkert, Beta, Brownstein, exponential-sphere and Persic models. The analysis is performed for eight galaxies under the assumption that RCs are dark matter dominated. The parameters are inferred from RC data and the relative statistical performance of the models is obtained through the Bayesian Information Criterion. We find that the Pad\'e profiles perform well, being comparable with the other profiles, albeit not universally preferred. In most galaxies, conventional two parameter profiles provide fits of comparable or better statistical quality, whereas the clearest improvement occurs for one particular galaxy, where the Pad\'e 03 profile gives the lowest BIC. Even though the Pad\'e profiles are often statistically less strong than other models, they appear plausible in explaining the dark matter nature. Hence, their empirical construction can therefore be used to reconstruct RCs phenomenologically.

Figures

Figures reproduced from arXiv: 2607.20262 by the authors.

Figure 1
Figure 1. FIG. 1: Observed galaxy RCs fitted using the new phenomenological DM models. [PITH_FULL_IMAGE:figures/full_fig_p014_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Observed galaxy RCs fitted using the new phenomenological DM models based on the Pad´e approximation. [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗

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Works this paper leans on

58 extracted references · 2 linked inside Pith

  1. [1]

    F. Zwicky. Die Rotverschiebung von extragalaktischen Nebeln.Helvetica Physica Acta, 6:110–127, January 1933

    1933

  2. [2]

    English and Spanish Translation of Zwicky’s (1933) The Redshift of Extragalactic Nebulae.arXiv e-prints, page arXiv:1711.01693, November 2017

    Heinz Andernach and Fritz Zwicky. English and Spanish Translation of Zwicky’s (1933) The Redshift of Extragalactic Nebulae.arXiv e-prints, page arXiv:1711.01693, November 2017

    arXiv 1933

  3. [3]

    V. C. Rubin, D. Burstein, Jr. Ford, W. K., and N. Thonnard. Rotation velocities of 16 SA galaxies and a comparison of Sa, SB and SC rotation properties.Astrophys. J., 289:81–104, 1985

    1985

  4. [4]

    Gonzalez, Maxim Markevitch, Scott W

    Douglas Clowe, Maruˇ sa Bradaˇ c, Anthony H. Gonzalez, Maxim Markevitch, Scott W. Randall, Christine Jones, and Dennis Zaritsky. A Direct Empirical Proof of the Existence of Dark Matter.Astrophys. J. Lett., 648(2):L109–L113, September 2006

    2006

  5. [5]

    Planck Collaboration and P. A. R. Ade et al. Planck Collaboration. Ade. Planck 2013 results. I. Overview of products and scientific results.Astron. Astrophys., 571:A1, 2014

    2013

  6. [6]

    Planck 2018 results

    Planck Collaboration and et.al. Planck 2018 results. I. Overview and the cosmological legacy of Planck.Astron. Astrophys., 641:A1, September 2020

    2018

  7. [7]

    A. Bosma. 21-cm line studies of spiral galaxies. I. Observations of the galaxies NGC 5033, 3198, 5055, 2841, and 7331. Astronomical. J., 86:1791–1824, December 1981. 12

    1981

  8. [8]

    A. Bosma. 21-cm line studies of spiral galaxies. II. The distribution and kinematics of neutral hydrogen in spiral galaxies of various morphological types.Astronomical. J., 86:1825–1846, December 1981

    1981

Show all 58 references
  1. [9]

    K. G. Begeman, A. H. Broeils, and R. H. Sanders. Extended rotation curves of spiral galaxies : dark haloes and modified dynamics.Mon. Not. Roy. Astr. Soc., 249:523, April 1991

    1991

  2. [10]

    Navarro, Carlos S

    Julio F. Navarro, Carlos S. Frenk, and Simon D. M. White. Simulations of X-ray clusters.Mon. Not. Roy. Astr. Soc., 275(3):720–740, 1995

    1995

  3. [11]

    Moore, F

    B. Moore, F. Governato, T. Quinn, J. Stadel, and G. Lake. Resolving the Structure of Cold Dark Matter Halos.Astrophys. J. Lett., 499(1):L5–L8, 1998

    1998

  4. [12]

    J. Einasto. On the Construction of a Composite Model for the Galaxy and on the Determination of the System of Galactic Parameters.Trudy Astrofizicheskogo Instituta Alma-Ata, 5:87–100, January 1965

    1965

  5. [13]

    Graham, Ben Moore, J¨ urg Diemand, and Balˇ sa Terzi´ c

    David Merritt, Alister W. Graham, Ben Moore, J¨ urg Diemand, and Balˇ sa Terzi´ c. Empirical models for dark matter halos. i. nonparametric construction of density profiles and comparison with parametric models.The Astronomical Journal, 132(6):2685–2700, 2006

    2006

  6. [14]

    Navarro, Aaron Ludlow, Volker Springel, Jie Wang, Mark Vogelsberger, Simon D

    Julio F. Navarro, Aaron Ludlow, Volker Springel, Jie Wang, Mark Vogelsberger, Simon D. M. White, Adrian Jenkins, Carlos S. Frenk, and Amina Helmi. The diversity and similarity of simulated cold dark matter haloes.Mon. Not. Roy. Astr. Soc., 402(1):21–34, February 2010

    2010

  7. [15]

    A. Burkert. The Structure of Dark Matter Halos in Dwarf Galaxies.Astrophys. J. Lett., 447:L25–L28, 1995

    1995

  8. [16]

    W. J. G. de Blok and S. S. McGaugh. The dark and visible matter content of low surface brightness disc galaxies.Mon. Not. Roy. Astr. Soc., 290(3):533–552, September 1997

    1997

  9. [17]

    The universal rotation curve of spiral galaxies — I

    Massimo Persic, Paolo Salucci, and Fulvio Stel. The universal rotation curve of spiral galaxies — I. The dark matter connection.Mon. Not. Roy. Astr. Soc., 281(1):27–47, July 1996

    1996

  10. [18]

    J. R. Brownstein and J. W. Moffat. Galaxy Rotation Curves without Nonbaryonic Dark Matter.Astrophys. J., 636(2):721– 741, 2006

    2006

  11. [19]

    Y. Sofue. Rotation Curve and Mass Distribution in the Galactic Center - From Black Hole to Entire Galaxy.Publications of the Astronomical Society of Japan, 65:118, 2013

    2013

  12. [20]

    Rotation Curve of the Milky Way and the Dark Matter Density.Galaxies, 8(2):37, 2020

    Yoshiaki Sofue. Rotation Curve of the Milky Way and the Dark Matter Density.Galaxies, 8(2):37, 2020

    2020

  13. [21]

    The Rotation Curves of Dwarf Galaxies: A Problem for Cold Dark Matter?Astrophys

    George Rhee, Octavio Valenzuela, Anatoly Klypin, Jon Holtzman, and Bhasker Moorthy. The Rotation Curves of Dwarf Galaxies: A Problem for Cold Dark Matter?Astrophys. J., 617(2):1059–1076, December 2004

    2004

  14. [22]

    R. A. Swaters, R. Sancisi, T. S. van Albada, and J. M. van der Hulst. The rotation curves shapes of late-type dwarf galaxies.Astron. Astrophys., 493(3):871–892, January 2009

    2009

  15. [23]

    Oman, Julio F

    Kyle A. Oman, Julio F. Navarro, Azadeh Fattahi, Carlos S. Frenk, Till Sawala, Simon D. M. White, Richard Bower, Robert A. Crain, Michelle Furlong, Matthieu Schaller, Joop Schaye, and Tom Theuns. The unexpected diversity of dwarf galaxy rotation curves.Mon. Not. Roy. Astr. Soc....

    2015

  16. [24]

    van den Bosch and Rob A

    Frank C. van den Bosch and Rob A. Swaters. Dwarf galaxy rotation curves and the core problem of dark matter haloes. Mon. Not. Roy. Astr. Soc., 325(3):1017–1038, August 2001

    2001

  17. [25]

    J. I. Read, G. Iorio, O. Agertz, and F. Fraternali. Understanding the shape and diversity of dwarf galaxy rotation curves in ΛCDM.Mon. Not. Roy. Astr. Soc., 462(4):3628–3645, November 2016

    2016

  18. [26]

    E. V. Karukes and P. Salucci. The universal rotation curve of dwarf disc galaxies.Mon. Not. Roy. Astr. Soc., 465(4):4703– 4722, March 2017

    2017

  19. [27]

    Santos-Santos, Arianna Di Cintio, Chris B

    Isabel M. Santos-Santos, Arianna Di Cintio, Chris B. Brook, Andrea Macci` o, Aaron Dutton, and Rosa Dom ´ ınguez-Tenreiro. NIHAO - XIV. Reproducing the observed diversity of dwarf galaxy rotation curve shapes in ΛCDM.Mon. Not. Roy. Astr. Soc., 473(4):4392–4403, February 2018

    2018

  20. [28]

    Koribalski

    Se-Heon Oh, Shinna Kim, Shin-Jeong Kim, and B¨ arbel S. Koribalski. Rotation curve analysis of dwarf galaxies from L VHIS.Astrophysics and Space Science, 370(11):129, November 2025

    2025

  21. [29]

    van den Bosch, Brant E

    Frank C. van den Bosch, Brant E. Robertson, Julianne J. Dalcanton, and W. J. G. de Blok. Constraints on the Structure of Dark Matter Halos from the Rotation Curves of Low Surface Brightness Galaxies.Astronomical. J., 119(4):1579–1591, April 2000

    2000

  22. [30]

    W. J. G. de Blok. Halo Mass Profiles and Low Surface Brightness Galaxy Rotation Curves.Astrophys. J., 634(1):227–238, November 2005

    2005

  23. [31]

    Hayashi, J

    E. Hayashi, J. F. Navarro, C. Power, A. Jenkins, C. S. Frenk, S. D. M. White, V. Springel, J. Stadel, and T. R. Quinn. The inner structure of ΛCDM haloes - II. Halo mass profiles and low surface brightness galaxy rotation curves.Mon. Not. Roy. Astr. Soc., 355(3):794–812, December 2004

    2004

  24. [32]

    The universal rotation curve of low surface brightness galaxies - IV

    Chiara Di Paolo, Paolo Salucci, and Adnan Erkurt. The universal rotation curve of low surface brightness galaxies - IV. The interrelation between dark and luminous matter.Mon. Not. Roy. Astr. Soc., 490(4):5451–5477, December 2019

    2019

  25. [33]

    McGaugh, and W

    Rachel Kuzio de Naray, Stacy S. McGaugh, and W. J. G. de Blok. Mass Models for Low Surface Brightness Galaxies with High-Resolution Optical Velocity Fields.Astrophys. J., 676(2):920–943, April 2008

    2008

  26. [34]

    Rotation and mass in the Milky Way and spiral galaxies.Publications of the Astronomical Society of Japan , 69(1):R1, February 2017

    Yoshiaki Sofue. Rotation and mass in the Milky Way and spiral galaxies.Publications of the Astronomical Society of Japan , 69(1):R1, February 2017

    2017

  27. [35]

    Boshkayev, T

    K. Boshkayev, T. Konysbayev, Ye. Kurmanov, M. Muccino, and Zhumakhanova G. Physical properties of dark matter in galaxy u11454.Physical Sciences and Technology, 10(3-4):11–20, 2020

    2020

  28. [36]

    Imprint of Pressure on Characteristic Dark Matter Profiles: The Case of ESO0140040.Galaxies, 8(4):74, October 2020

    Kuantay Boshkayev, Talgar Konysbayev, Ergali Kurmanov, Orlando Luongo, and Marco Muccino. Imprint of Pressure on Characteristic Dark Matter Profiles: The Case of ESO0140040.Galaxies, 8(4):74, October 2020

    2020

  29. [37]

    Boshkayev, T

    K. Boshkayev, T. Konysbayev, E. Kurmanov, O. Luongo, D. Malafarina, K. Mutalipova, and G. Zhumakhanova. Effects of non-vanishing dark matter pressure in the Milky Way Galaxy.Mon. Not. Roy. Astr. Soc., 508(1):1543–1554, November 13 2021

    2021

  30. [38]

    Kurmanov, T

    Ye. Kurmanov, T. Boshkayev, K.and Konysbayev, M. Muccino, A. Urazalina, G. Ikhsan, N. Saiyp, G. Rabigulova, M. Kar- linova, G. Suliyeva, and N. Beissen. Analysis of dark matter profiles in the halos of spiral galaxies.Physical Sciences and Technology, 10(3-4):4–16, 2023

    2023

  31. [39]

    Numerical analyses of M31 dark matter profiles.International Journal of Modern Physics D, 33:2450016, January 2024

    Kuantay Boshkayev, Talgar Konysbayev, Yergali Kurmanov, Orlando Luongo, Marco Muccino, Hernando Quevedo, and Gulnur Zhumakhanova. Numerical analyses of M31 dark matter profiles.International Journal of Modern Physics D, 33:2450016, January 2024

    2024

  32. [40]

    Study of Various Dark Matter Halo Profiles in Milky Way and M31 Galaxies within the Standard Cosmology Framework.Research in Astronomy and Astrophysics, 25(7):075005, July 2025

    Darshan Kumar, Nisha Rani, Deepak Jain, Shobhit Mahajan, and Amitabha Mukherjee. Study of Various Dark Matter Halo Profiles in Milky Way and M31 Galaxies within the Standard Cosmology Framework.Research in Astronomy and Astrophysics, 25(7):075005, July 2025

    2025

  33. [41]

    T. S. van Albada, J. N. Bahcall, K. Begeman, and R. Sancisi. Distribution of dark matter in the spiral galaxy NGC 3198. Astrophys. J., 295:305–313, August 1985

    1985

  34. [42]

    W. J. G. de Blok, Stacy S. McGaugh, and Vera C. Rubin. High-Resolution Rotation Curves of Low Surface Brightness Galaxies. II. Mass Models.Astronomical. J., 122(5):2396–2427, November 2001

    2001

  35. [43]

    Gentile, P

    G. Gentile, P. Salucci, U. Klein, D. Vergani, and P. Kalberla. The cored distribution of dark matter in spiral galaxies. Mon. Not. Roy. Astr. Soc., 351(3):903–922, July 2004

    2004

  36. [44]

    W. J. G. de Blok, F. Walter, E. Brinks, C. Trachternach, S.-H. Oh, and R. C. Kennicutt, Jr. High-Resolution Rotation Curves and Galaxy Mass Models from THINGS.Astronomical. J., 136(6):2648–2719, December 2008

    2008

  37. [45]

    T. S. van Albada and R. Sancisi. Dark Matter in Spiral Galaxies.Philosophical Transactions of the Royal Society of London Series A, 320(1556):447–464, December 1986

    1986

  38. [46]

    Se-Heon Oh, Chris Brook, Fabio Governato, Elias Brinks, Lucio Mayer, W. J. G. de Blok, Alyson Brooks, and Fabian Walter. The Central Slope of Dark Matter Cores in Dwarf Galaxies: Simulations versus THINGS.Astronomical. J., 142(1):24, July 2011

    2011

  39. [47]

    Baker and Peter Graves-Morris.Pade approximants

    George A. Baker and Peter Graves-Morris.Pade approximants. Part 1: Basic theory. Cambridge University Press, 1981

    1981

  40. [48]

    Baker and Peter Graves-Morris.Pade approximants

    George A. Baker and Peter Graves-Morris.Pade approximants. Part 2: Extensions and applications. Addison-Wesley Pub Co, 1981

    1981

  41. [49]

    Iyer, and B

    Thibault Damour, Bala R. Iyer, and B. S. Sathyaprakash. Improved filters for gravitational waves from inspiraling compact binaries.Phys. Rev. D, 57(2):885–907, January 1998

    1998

  42. [50]

    Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation.Phys

    Thibault Damour, Piotr Jaranowski, and Gerhard Sch¨ afer. Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation.Phys. Rev. D, 62(4):044024, August 2000

    2000

  43. [51]

    Cosmographic analysis of the equation of state of the universe through Pad´ e approximations.Phys

    Christine Gruber and Orlando Luongo. Cosmographic analysis of the equation of state of the universe through Pad´ e approximations.Phys. Rev. D, 89(10):103506, May 2014

    2014

  44. [52]

    Precision cosmology with Pad´ e rational approximations: Theoretical predictions versus observational limits.Phys

    Alejandro Aviles, Alessandro Bravetti, Salvatore Capozziello, and Orlando Luongo. Precision cosmology with Pad´ e rational approximations: Theoretical predictions versus observational limits.Phys. Rev. D, 90(4):043531, August 2014

    2014

  45. [53]

    Cosmological applications of Pad´ e approximant.Journal of Cosmology and Astroparticle Physics, 2014(1):045, January 2014

    Hao Wei, Xiao-Peng Yan, and Ya-Nan Zhou. Cosmological applications of Pad´ e approximant.Journal of Cosmology and Astroparticle Physics, 2014(1):045, January 2014

    2014

  46. [54]

    Raul Jimenez, Licia Verde, and S. Peng Oh. Dark halo properties from rotation curves.Mon. Not. Roy. Astr. Soc., 339(1):243–259, 2003

    2003

  47. [55]

    Barranco, A

    J. Barranco, A. Bernal, and D. N´ u˜ nez. Dark matter equation of state from rotational curves of galaxies.Mon. Not. Roy. Astr. Soc., 449(1):403–413, 2015

    2015

  48. [56]

    Baker and Peter Graves-Morris.Pad´ e Approximants

    George A. Baker and Peter Graves-Morris.Pad´ e Approximants. Cambridge University Press, 2nd edition, 1996

    1996

  49. [57]

    Suliyeva, Ye.B

    G.B. Suliyeva, Ye.B. Kurmanov, T.K. Konysbayev, K.A. Boshkayev, A.A. Urazalina, and O. Luongo. Finite temperature effects within scalar field dark matter model.Eurasian Physical Technical Journal, 21(2(48)):92–101, June 2024

    2024

  50. [58]

    Testing Scalar Field Dark Matter models in M31 galaxy through the Rotation Curve analysis.arXiv e-prints, page arXiv:2604.23353, April 2026

    Gulnara Suliyeva, Kuantay Boshkayev, Talgar Konysbayev, Yergali Kurmanov, and Guldana Rabigulova. Testing Scalar Field Dark Matter models in M31 galaxy through the Rotation Curve analysis.arXiv e-prints, page arXiv:2604.23353, April 2026. 14 Beta Brownstein Burkert Exponential...

    2026 arXiv

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Reviewed August 1, 2026 · model on record in the stance chip above.