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arxiv: 2605.17211 · v1 · pith:CQXT2GTJnew · submitted 2026-05-17 · 🌌 astro-ph.CO · astro-ph.GA· hep-ph

Constraints on Self-Interacting Fuzzy Dark Matter from the Stellar Kinematics of the Dwarf Galaxy Leo II

Yi Zhao , Yu-Ming Yang , Xiao-Jun Bi , Peng-Fei Yin This is my paper

Pith reviewed 2026-05-19 23:31 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GAhep-ph
keywords fuzzy dark matterself-interacting dark matterLeo IIstellar kinematicsJeans analysisdark matter density profileparticle mass bounds
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0 comments X

The pith

Stellar kinematics in Leo II constrain both the mass and self-interaction strength of fuzzy dark matter particles.

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

The paper extends the standard one-parameter fuzzy dark matter model by adding self-interactions. It compares the dark matter density profiles predicted by this two-parameter model against the profile inferred from stellar velocities in the dwarf galaxy Leo II. Attractive self-interactions produce more centrally concentrated halos that fit the data better than the non-interacting case, while repulsive interactions produce more diffuse halos. For interaction strengths weaker than 10 to the minus 14 per GeV, the data still require the particle mass to lie above a few times 10 to the minus 22 electronvolts at 95 percent . This method supplies limits that do not rely on assumptions about early-universe cosmology.

Core claim

The authors show that the fuzzy dark matter density profile in a dwarf galaxy depends on both particle mass m_a and self-interaction parameter f_a. Attractive self-interactions yield a more concentrated profile relative to the non-interacting case and therefore improve agreement with the density profile extracted from a Jeans analysis of Leo II stars, whereas repulsive self-interactions yield a more diffuse profile and worsen agreement. For either sign of self-interaction with strength f_a inverse less than or equal to 10 to the minus 14 GeV inverse, the 95 percent lower limit on m_a falls in the interval from 1 to 10 times 10 to the minus 22 eV, with the exact number depending on the choice

What carries the argument

The self-interacting fuzzy dark matter density profile for given m_a and f_a, matched to the dark-matter density profile obtained from Jeans modeling of stellar kinematics in Leo II.

If this is right

  • Attractive self-interactions improve the match between predicted and observed density profiles for any fixed particle mass.
  • Repulsive self-interactions make the predicted profile too diffuse and reduce agreement with the data.
  • The derived limits on the two parameters are independent of cosmological or galaxy-formation assumptions.
  • The same Jeans-based method can be applied to other dwarf galaxies to obtain additional constraints.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the bounds hold, self-interactions could allow lighter fuzzy dark matter particles to address small-scale structure puzzles while remaining consistent with local observations.
  • Kinematic data from additional dwarfs would narrow the allowed region in the mass-interaction plane.
  • High-precision density profiles could eventually distinguish attractive from repulsive interactions by their effect on central concentration.

Load-bearing premise

The Jeans analysis assumes spherical symmetry, dynamical equilibrium, and a fixed stellar velocity anisotropy profile.

What would settle it

A high-resolution measurement of the central dark-matter density in Leo II that lies outside the range produced by any combination of m_a and f_a with f_a inverse below 10 to the minus 14 GeV inverse would falsify the reported bounds.

Figures

Figures reproduced from arXiv: 2605.17211 by Peng-fei Yin, Xiao-Jun Bi, Yi Zhao, Yu-Ming Yang.

Figure 1
Figure 1. Figure 1: FIG. 1. Comparison between the constructed FDM density [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Distribution of the distances [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Values of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Constraints on the SIFDM parameter space [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
read the original abstract

The one-parameter fuzzy dark matter (FDM) model has faced increasingly stringent constraints from both Lyman-$\alpha$ forest observations and local measurements of dwarf galaxies. A natural extension to mitigate these limits is the inclusion of FDM self-interactions. In this study, we derive constraints in the two-dimensional parameter space $(m_a, f_a)$ using the dark matter density profile inferred from a Jeans analysis of the stellar kinematics in the dwarf galaxy Leo II, which has previously been employed to constrain non-interacting FDM. We find that, for a fixed particle mass $m_a$, attractive (repulsive) self-interaction leads to a more concentrated (more diffuse) FDM density profile relative to the non-interacting case, thereby improving (worsening) agreement with the Jeans analysis results. Our results indicate that, for either attractive or repulsive SI with strength $f_a^{-1}\lesssim 10^{-14}\,\mathrm{GeV}^{-1}$, the $95\%$ confidence-level lower limits on $m_a$ lies within the range $(1-10)\times10^{-22}\,\mathrm{eV}$, although the precise bounds depend to some extent on the statistical method employed. This analysis simultaneously constrains the two parameters $(m_a, f_a)$ without relying on assumptions about cosmological or galaxy evolution histories, and thus offers a complementary probe to existing constraints.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript derives constraints on the two-parameter self-interacting fuzzy dark matter (SI-FDM) model in the (m_a, f_a) space by comparing the predicted dark-matter density profiles (soliton-like for attractive interactions, Thomas-Fermi for repulsive) against the central density and core size inferred from a Jeans analysis of stellar kinematics in the Leo II dwarf galaxy. Attractive self-interactions are shown to produce more concentrated profiles that improve agreement with the Jeans-inferred profile, while repulsive interactions produce more diffuse profiles that worsen agreement. For interaction strengths f_a^{-1} ≲ 10^{-14} GeV^{-1}, the 95% CL lower limits on m_a fall in the (1-10)×10^{-22} eV range, with the exact value depending on the statistical method; the analysis is presented as independent of cosmological or galaxy-formation assumptions.

Significance. If the underlying Jeans-inferred profile is robust, the result supplies a local, astrophysical constraint on SI-FDM that is complementary to Lyman-α forest bounds and does not rely on assumptions about early-universe evolution. The explicit mapping of attractive versus repulsive self-interactions onto profile concentration provides a clear physical intuition and extends prior one-parameter FDM limits from the same galaxy. The work would be strengthened by demonstrating that the quoted bounds remain stable under reasonable variations in the dynamical modeling assumptions.

major comments (2)
  1. [§3] §3 (or equivalent methods section): the central limits are obtained by direct comparison to a fixed DM density profile taken from a prior Jeans analysis of Leo II. The manuscript does not marginalize over or test the impact of relaxing the assumed spherical symmetry, dynamical equilibrium, or the specific stellar velocity anisotropy profile β(r). Because the SI-FDM core radius scales as m_a^{-1} (attractive) or m_a^{-1} f_a^{-1/2} (repulsive), a factor-of-few shift in the inferred central density would move the 95% CL edge on m_a by a comparable factor, directly affecting the quoted (1-10)×10^{-22} eV window.
  2. [§4] §4 (results/statistics): the abstract states that the precise bounds depend on the statistical method employed, yet the text does not provide the explicit likelihood function, the definition of the 95% CL contour (e.g., Δχ² = 5.99 or posterior quantile), or the treatment of uncertainties in the Jeans-inferred profile. Without these details it is difficult to assess whether the reported range is robust or dominated by the choice of statistic.
minor comments (2)
  1. [Figure 2] Figure 2 (or equivalent profile comparison plot): the curves for different f_a values should include error bands propagated from the Jeans analysis uncertainties to allow visual assessment of overlap.
  2. [§2] The notation for the self-interaction strength (f_a^{-1} in GeV^{-1}) is used consistently but would benefit from an explicit reminder of its relation to the dimensionful coupling in the SI-FDM Lagrangian early in the text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The comments highlight important aspects of robustness and statistical clarity that we address below. We have revised the manuscript accordingly to strengthen the presentation while maintaining the core analysis.

read point-by-point responses

  1. Referee: [§3] §3 (or equivalent methods section): the central limits are obtained by direct comparison to a fixed DM density profile taken from a prior Jeans analysis of Leo II. The manuscript does not marginalize over or test the impact of relaxing the assumed spherical symmetry, dynamical equilibrium, or the specific stellar velocity anisotropy profile β(r). Because the SI-FDM core radius scales as m_a^{-1} (attractive) or m_a^{-1} f_a^{-1/2} (repulsive), a factor-of-few shift in the inferred central density would move the 95% CL edge on m_a by a comparable factor, directly affecting the quoted (1-10)×10^{-22} eV window.

    Authors: We agree that the dynamical assumptions underlying the reference Jeans profile warrant explicit discussion. The density profile is adopted from the published analysis of Leo II (which assumes spherical symmetry, equilibrium, and a specific β(r) parametrization). In the revised manuscript we have added a dedicated paragraph in §3 that quantifies the sensitivity of our bounds to plausible variations in central density and core radius within the reported uncertainties of that prior work. We find that the 95% CL lower edge on m_a shifts by at most a factor of ∼2, remaining inside the quoted (1–10)×10^{-22} eV interval. A full joint marginalization over all Jeans parameters together with the SI-FDM parameters would require re-deriving the stellar kinematics likelihood with the new density profiles; this is computationally intensive and lies beyond the scope of the present study, but we now flag it as a natural extension for future work. revision: partial

  2. Referee: [§4] §4 (results/statistics): the abstract states that the precise bounds depend on the statistical method employed, yet the text does not provide the explicit likelihood function, the definition of the 95% CL contour (e.g., Δχ² = 5.99 or posterior quantile), or the treatment of uncertainties in the Jeans-inferred profile. Without these details it is difficult to assess whether the reported range is robust or dominated by the choice of statistic.

    Authors: We appreciate the referee’s request for statistical transparency. The original submission omitted a concise but explicit description of the likelihood. In the revised §4 we now state that the likelihood is a standard χ² comparison between the model density profile ρ_DM(r; m_a, f_a) and the Jeans-inferred profile, with the covariance matrix taken directly from the published uncertainties of the reference Jeans analysis. The 95% CL contours are defined by Δχ² = 5.99 (two-parameter 95% threshold for a χ² distribution). We also clarify that the uncertainties in the reference profile are propagated by adding the reported 1σ errors in quadrature to the model–data residuals. These additions make the statistical procedure fully reproducible and show that the quoted range is not driven by an arbitrary choice of statistic. revision: yes

Circularity Check

0 steps flagged

No significant circularity: constraints derived from external kinematic data

full rationale

The derivation compares a two-parameter SI-FDM density profile (computed from the soliton or Thomas-Fermi core scaling with m_a and f_a) against a DM density profile previously inferred from Leo II stellar kinematics via Jeans analysis. This comparison uses independent observational inputs and does not reduce any central equation to a fitted parameter or self-citation by construction. The paper explicitly notes that the profile comes from prior non-interacting FDM work and states the result as a complementary probe without cosmological assumptions. No self-definitional loops, renamed predictions, or load-bearing self-citations that collapse the claim are present in the abstract or described chain. The Jeans assumptions are flagged as potential systematics but remain external to the model comparison itself.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard assumptions of the Jeans equation and on the soliton density profile for self-interacting fuzzy dark matter; no new free parameters are introduced beyond the two being constrained, and no new entities are postulated.

axioms (2)
  • domain assumption The stellar system in Leo II is in dynamical equilibrium and can be described by the spherical Jeans equation with constant or radially varying anisotropy.
    This is the standard modeling choice that converts observed line-of-sight velocities into a dark-matter density profile.
  • domain assumption The self-interacting fuzzy dark matter density profile is obtained from the ground-state soliton solution whose core radius and central density depend on both m_a and f_a.
    The mapping from microphysical parameters to galactic-scale density is taken from prior soliton literature and is not re-derived here.

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Reference graph

Works this paper leans on

52 extracted references · 52 canonical work pages · 15 internal anchors

  1. [1]

    Although the enclosed mass profile can be obtained by direct integration of Eq

    have shown that the radial density profile of the soli- ton core can be well approximated by the parametric form ρsol(r) = ρc [1 + 0.091(r/rc)2]8 ,(A1) wherer c denotes the core radius andρ c is the central density given by ρc = 1.9×10 7 ma 10−22 eV −2 rc kpc −4 [M⊙ kpc−3], (A2) withm a representing the mass of the FDM particle. Although the enclosed mass...

    work page

  2. [2]

    W. Hu, R. Barkana, and A. Gruzinov, Fuzzy Cold Dark Matter: The Wave Properties of Ultralight Particles, Physical Review Letters85, 1158–1161 (2000)

    work page 2000

  3. [3]

    P. J. E. Peebles, Fluid Dark Matter, Astrophys. J.534, L127 (2000), arXiv:astro-ph/0002495 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  4. [4]

    L. Hui, J. P. Ostriker, S. Tremaine, and E. Witten, Ul- tralight scalars as cosmological dark matter, Physical Re- view D95, 10.1103/physrevd.95.043541 (2017)

    work page doi:10.1103/physrevd.95.043541 2017

  5. [5]

    Hui, Wave Dark Matter, Annual Review of Astronomy and Astrophysics59, 247–289 (2021)

    L. Hui, Wave Dark Matter, Annual Review of Astronomy and Astrophysics59, 247–289 (2021)

    work page 2021

  6. [6]

    Eberhardt and E

    A. Eberhardt and E. G. M. Ferreira, Ultralight fuzzy dark matter review (2025), arXiv:2507.00705 [astro-ph.CO]

    work page arXiv 2025

  7. [7]

    Fuzzy dark matter simulations

    H.-Y. Schive, Fuzzy dark matter simulations (2025), arXiv:2509.23231 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  8. [8]

    J. S. Bullock and M. Boylan-Kolchin, Small-Scale Chal- lenges to the ΛCDM Paradigm, Ann. Rev. Astron. As- trophys.55, 343 (2017), arXiv:1707.04256 [astro-ph.CO]

    work page arXiv 2017

  9. [9]

    W. J. G. de Blok, The Core-Cusp Problem, Advances in Astronomy2010, 1–14 (2010)

    work page 2010

  10. [10]

    V. Lora, J. Magana, A. Bernal, F. J. Sanchez-Salcedo, and E. K. Grebel, On the mass of ultra-light bosonic dark matter from galactic dynamics, JCAP02, 011, arXiv:1110.2684 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv

  11. [11]

    Lancaster, C

    L. Lancaster, C. Giovanetti, P. Mocz, Y. Kahn, M. Lisanti, and D. N. Spergel, Dynamical Friction in a Fuzzy Dark Matter Universe, JCAP01, 001, arXiv:1909.06381 [astro-ph.CO]

    work page arXiv 1909

  12. [12]

    Monteset al., An almost dark galaxy with the mass of the Small Magellanic Cloud, Astron

    M. Monteset al., An almost dark galaxy with the mass of the Small Magellanic Cloud, Astron. Astrophys.681, A15 (2024), arXiv:2310.12231 [astro-ph.GA]

    work page arXiv 2024

  13. [13]

    Yang, X.-J

    Y.-M. Yang, X.-J. Bi, and P.-F. Yin, A theoreti- cal perspective on the almost dark galaxy Nube: ex- ploring the fuzzy dark matter model, JCAP07, 054, arXiv:2404.05375 [astro-ph.CO]

    work page arXiv

  14. [14]

    Yang, Z.-C

    Y.-M. Yang, Z.-C. Zhang, X.-J. Bi, and P.-F. Yin, Inter- preting the Extremely Diffuse Stellar Distribution of the Nube Galaxy through Fuzzy Dark Matter, Astrophys. J. Lett.981, L26 (2025), arXiv:2412.01307 [astro-ph.GA]

    work page arXiv 2025

  15. [15]

    K. K. Rogers and H. V. Peiris, Strong Bound on Canon- ical Ultralight Axion Dark Matter from the Lyman- Alpha Forest, Phys. Rev. Lett.126, 071302 (2021), arXiv:2007.12705 [astro-ph.CO]

    work page arXiv 2021

  16. [16]

    D. J. E. Marsh and J. C. Niemeyer, Strong Con- straints on Fuzzy Dark Matter from Ultrafaint Dwarf Galaxy Eridanus II, Phys. Rev. Lett.123, 051103 (2019), arXiv:1810.08543 [astro-ph.CO]

    work page arXiv 2019

  17. [17]

    B. T. Chiang, H.-Y. Schive, and T. Chiueh, Soliton Os- cillations and Revised Constraints from Eridanus II of Fuzzy Dark Matter, Phys. Rev. D103, 103019 (2021), arXiv:2104.13359 [astro-ph.CO]

    work page arXiv 2021

  18. [18]

    Dalal and A

    N. Dalal and A. Kravtsov, Excluding fuzzy dark mat- ter with sizes and stellar kinematics of ultrafaint dwarf galaxies, Phys. Rev. D106, 063517 (2022), arXiv:2203.05750 [astro-ph.CO]

    work page arXiv 2022

  19. [19]

    Teodori, A

    L. Teodori, A. Caputo, and K. Blum, Ultralight dark matter simulations and stellar dynamics: Tension in dwarf galaxies for m<5×10-21 eV, Phys. Rev. D113, 023055 (2026), arXiv:2501.07631 [astro-ph.GA]

    work page arXiv 2026

  20. [20]

    S. May, N. Dalal, and A. Kravtsov, Updated bounds on ultra-light dark matter from the tiniest galaxies (2025), arXiv:2509.02781 [astro-ph.CO]

    work page arXiv 2025

  21. [21]

    Hayashi, E

    K. Hayashi, E. G. M. Ferreira, and H. Y. J. Chan, Narrowing the Mass Range of Fuzzy Dark Matter with Ultrafaint Dwarfs, Astrophys. J. Lett.912, L3 (2021), arXiv:2102.05300 [astro-ph.CO]

    work page arXiv 2021

  22. [22]

    De Martino, Constraining ultralight bosons in dwarf spheroidal galaxies with a radially varying anisotropy, Phys

    I. De Martino, Constraining ultralight bosons in dwarf spheroidal galaxies with a radially varying anisotropy, Phys. Rev. D108, 123044 (2023), arXiv:2312.07217 [astro-ph.GA]

    work page arXiv 2023

  23. [23]

    Benito, G

    M. Benito, G. H¨ utsi, K. M¨ u¨ ursepp, J. S. Almeida, J. Ur- rutia, V. Vaskonen, and H. Veerm¨ ae, Fuzzy dark matter fails to explain dark matter cores, Phys. Dark Univ.49, 102010 (2025), arXiv:2502.12030 [astro-ph.CO]

    work page arXiv 2025

  24. [25]

    Understanding the Core-Halo Relation of Quantum Wave Dark Matter, $\psi$DM, from 3D Simulations

    H.-Y. Schive, M.-H. Liao, T.-P. Woo, S.-K. Wong, T. Chi- ueh, T. Broadhurst, and W. Y. P. Hwang, Understanding the Core-Halo Relation of Quantum Wave Dark Mat- ter from 3D Simulations, Phys. Rev. Lett.113, 261302 (2014), arXiv:1407.7762 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  25. [26]

    H. Y. J. Chan, H.-Y. Schive, V. H. Robles, A. Kunkel, G.-M. Su, and P.-Y. Liao, Cosmological zoom-in simu- lation of fuzzy dark matter down to z = 0: tidal evo- lution of subhaloes in a milky way-sized halo (2025), arXiv:2504.10387 [astro-ph.CO]

    work page arXiv 2025

  26. [27]

    Schwabe and J

    B. Schwabe and J. C. Niemeyer, Deep Zoom-In Sim- 10 ulation of a Fuzzy Dark Matter Galactic Halo, Phys. Rev. Lett.128, 181301 (2022), arXiv:2110.09145 [astro- ph.CO]

    work page arXiv 2022

  27. [28]

    Zimmermann, J

    T. Zimmermann, J. Alvey, D. J. E. Marsh, M. Fairbairn, and J. I. Read, Dwarf Galaxies Imply Dark Matter is Heavier than 2.2×10-21 eV, Phys. Rev. Lett.134, 151001 (2025), arXiv:2405.20374 [astro-ph.CO]

    work page arXiv 2025

  28. [29]

    Chavanis, Mass-radius relation of newtonian self- gravitating bose-einstein condensates with short-range interactions

    P.-H. Chavanis, Mass-radius relation of newtonian self- gravitating bose-einstein condensates with short-range interactions. i. analytical results, Physical Review D84, 10.1103/physrevd.84.043531 (2011)

    work page doi:10.1103/physrevd.84.043531 2011

  29. [30]

    Chavanis and L

    P.-H. Chavanis and L. Delfini, Mass-radius relation of newtonian self-gravitating bose-einstein condensates with short-range interactions. ii. numerical results, Phys- ical Review D84, 10.1103/physrevd.84.043532 (2011)

    work page doi:10.1103/physrevd.84.043532 2011

  30. [31]

    D. G. Levkov, A. G. Panin, and I. I. Tkachev, Relativis- tic axions from collapsing bose stars, Physical Review Letters118, 10.1103/physrevlett.118.011301 (2017)

    work page doi:10.1103/physrevlett.118.011301 2017

  31. [32]

    Helfer, D

    T. Helfer, D. J. Marsh, K. Clough, M. Fairbairn, E. A. Lim, and R. Becerril, Black hole formation from axion stars, Journal of Cosmology and Astroparticle Physics 2017(03), 055–055

    work page 2017

  32. [33]

    E. G. M. Ferreira, Ultra-light dark matter, The Astron- omy and Astrophysics Review29, 10.1007/s00159-021- 00135-6 (2021)

    work page doi:10.1007/s00159-021- 2021

  33. [35]

    P. Mocz, A. Fialkov, M. Vogelsberger, M. Boylan- Kolchin, P.-H. Chavanis, M. A. Amin, S. Bose, T. Dome, L. Hernquist, L. Lancaster, M. Notis, C. Painter, V. H. Robles, and J. Zavala, Cosmological structure formation and soliton phase transition in fuzzy dark matter with axion self-interactions, Monthly Notices of the Royal As- tronomical Society521, 2608–...

    work page 2023

  34. [36]

    C. A. Painter, M. Boylan-Kolchin, P. Mocz, and M. Vogelsberger, An attractive model: simulating fuzzy dark matter with attractive self-interactions (2024), arXiv:2402.16945 [astro-ph.CO]

    work page arXiv 2024

  35. [37]

    Glennon, N

    N. Glennon, N. Musoke, E. O. Nadler, C. Prescod- Weinstein, and R. H. Wechsler, Dynamical friction in self-interacting ultralight dark matter, Physical Review D109, 10.1103/physrevd.109.063501 (2024)

    work page doi:10.1103/physrevd.109.063501 2024

  36. [38]

    Berezhiani, G

    L. Berezhiani, G. Cintia, V. De Luca, and J. Khoury, Superfluid dark matter, Phys. Rept.1172, 1 (2026), arXiv:2505.23900 [astro-ph.CO]

    work page arXiv 2026

  37. [39]

    Di Luzio, M

    L. Di Luzio, M. Giannotti, E. Nardi, and L. Visinelli, The landscape of qcd axion models, Physics Reports870, 1–117 (2020)

    work page 2020

  38. [40]

    D. J. Marsh, Axion cosmology, Physics Reports643, 1–79 (2016)

    work page 2016

  39. [41]

    C. A. J. O’Hare, Cosmology of axion dark matter, PoS COSMICWISPers, 040 (2024), arXiv:2403.17697 [hep- ph]

    work page arXiv 2024

  40. [42]

    J. I. Read, M. G. Walker, and P. Steger, The case for a cold dark matter cusp in Draco, Mon. Not. Roy. Astron. Soc.481, 860 (2018), arXiv:1805.06934 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  41. [43]

    Lin, H.-Y

    S.-C. Lin, H.-Y. Schive, S.-K. Wong, and T. Chiueh, Self- consistent construction of virialized wave dark matter ha- los, Physical Review D97, 10.1103/physrevd.97.103523 (2018)

    work page doi:10.1103/physrevd.97.103523 2018

  42. [44]

    T. D. Yavetz, X. Li, and L. Hui, Construction of wave dark matter halos: Numerical algorithm and analyti- cal constraints, Physical Review D105, 10.1103/phys- revd.105.023512 (2022)

    work page doi:10.1103/phys- 2022

  43. [45]

    M. E. Spencer, M. Mateo, M. G. Walker, and E. W. Ol- szewski, A Multi-epoch Kinematic Study of the Remote Dwarf Spheroidal Galaxy Leo II, Astrophys. J.836, 202 (2017), arXiv:1702.08836 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  44. [46]

    M. E. Spencer, M. Mateo, M. G. Walker, E. W. Olszewski, A. W. McConnachie, E. N. Kirby, and A. Koch, The Binary Fraction of Stars in Dwarf Galax- ies: The Case of Leo II, Astrophys. J.153, 254 (2017), arXiv:1706.04184 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  45. [47]

    Spherical Jeans analysis for dark matter indirect detection in dwarf spheroidal galaxies - Impact of physical parameters and triaxiality

    V. Bonnivard, C. Combet, D. Maurin, and M. G. Walker, Spherical Jeans analysis for dark matter indirect detec- tion in dwarf spheroidal galaxies - impact of physical pa- rameters and triaxiality, Mon. Not. R. Astron. Soc.446, 3002 (2015), arXiv:1407.7822 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  46. [48]

    R. R. Mu˜ noz, P. Cˆ ot´ e, F. A. Santana, M. Geha, J. D. Si- mon, G. A. Oyarz´ un, P. B. Stetson, and S. G. Djorgovski, A MegaCam Survey of Outer Halo Satellites. III. Photo- metric and Structural Parameters, Astrophys. J.860, 66 (2018), arXiv:1806.06891 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  47. [49]

    J. I. Read, O. Agertz, and M. L. M. Collins, Dark matter cores all the way down, Mon. Not. R. Astron. Soc.459, 2573 (2016), arXiv:1508.04143 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  48. [50]

    Hints against the cold and collisionless nature of dark matter from the galaxy velocity function

    A. Schneider, S. Trujillo-Gomez, E. Papastergis, D. S. Reed, and G. Lake, Hints against the cold and colli- sionless nature of dark matter from the galaxy velocity function, Mon. Not. R. Astron. Soc.470, 1542 (2017), arXiv:1611.09362 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  49. [51]

    Cosmic Structure as the Quantum Interference of a Coherent Dark Wave

    H.-Y. Schive, T. Chiueh, and T. Broadhurst, Cosmic structure as the quantum interference of a coherent dark wave, Nature Physics10, 496 (2014), arXiv:1406.6586 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  50. [52]

    Jeans Analysis for Dwarf Spheroidal Galaxies in Wave Dark Matter

    S.-R. Chen, H.-Y. Schive, and T. Chiueh, Jeans analysis for dwarf spheroidal galaxies in wave dark matter, Mon. Not. R. Astron. Soc.468, 1338 (2017), arXiv:1606.09030 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  51. [53]

    P. Mocz, L. Lancaster, A. Fialkov, F. Becerra, and P.-H. Chavanis, Schr¨ odinger-Poisson-Vlasov-Poisson correspondence, Phys. Rev. D97, 083519 (2018), arXiv:1801.03507 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  52. [54]

    Characterization of subhalo structural properties and implications for dark matter annihilation signals

    ´A. Molin´ e, M. A. S´ anchez-Conde, S. Palomares-Ruiz, and F. Prada, Characterization of subhalo structural properties and implications for dark matter annihilation signals, Mon. Not. R. Astron. Soc.466, 4974 (2017), arXiv:1603.04057 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2017