Pith. sign in

REVIEW 3 major objections 4 minor 1 cited by

Tidal Suppression of Fuzzy Dark Matter Heating in Milky Way Satellite Galaxies

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper claims that including Milky Way and Large Magellanic Cloud tides in Fornax simulations suppresses fuzzy-dark-matter heating enough that $m_a \sim 10^{-22}$ eV matches observed size and velocity dispersion, relaxing earlier mass…

desk verdict Real step forward in simulating FDM heating with tides, but the relaxed mass bound is tied to hand-tuned initial conditions and an omitted host-granule effect. read the letter →

arxiv 2507.01686 v2 pith:J2BNQS3P submitted 2025-07-02 astro-ph.CO astro-ph.GAhep-ph

Yu-Ming Yang , Zhao-Chen Zhang , Xiao-Jun Bi , Peng-Fei Yin This is my paper
classification astro-ph.COastro-ph.GAhep-ph PACS 95.35.+d
keywords fuzzydarkmatterultralightscalarfieldFornaxdwarfgalaxytidalstrippingdynamicalheatingSchrodinger-Poissonsystemsatellitegalaxies
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

Fuzzy dark matter (FDM) is an ultralight bosonic dark matter whose quantum wavelength can reach kiloparsec scales, making its density fluctuate in granules that heat stars and puff out dwarf galaxies. Earlier studies of Milky Way satellites found no such heating and used that to rule out particle masses near $10^{-22}$ eV. This paper argues that those studies ignored the Milky Way's tidal field, and shows that when the tidal fields of both the Milky Way and the Large Magellanic Cloud are included, a simulated Fornax with $m_a = 10^{-22}$ eV keeps its half-light radius and velocity dispersion close to observed values. The result, if correct, relaxes previously stringent lower bounds on the FDM particle mass from satellite galaxies.

What carries the argument

The mechanism is the interplay between the satellite's wave function and the external tide. FDM is evolved as a Schrodinger-Poisson wave function while stars are $10^5$ point particles; the Milky Way's six-component potential and the LMC's cuspy profile enter as a tidal potential computed in the satellite's rest frame and added to self-gravity. The initial halo is built by eigenstate decomposition into a soliton core plus an outer NFW-like envelope, and it is the envelope's excited states that tidal forces strip away, removing the interference patterns responsible for heating. The quantity carrying the argument is the tidal potential of Eq. (1); its strength is varied through two orbital realizations bracketing weak and strong tides.

What would settle it

Decisive test: a zoom-in simulation of the same Fornax model in which the Milky Way's halo is also treated as fuzzy dark matter with $m_a = 10^{-22}$ eV; if the half-light radius or line-of-sight velocity dispersion still exceeds the observed $1\sigma$ bands after 10 Gyr, the tidal-suppression claim would be falsified.

Watch

Extended reading notes

Core claim

The central claim is that tidal stripping of the outer NFW-like part of Fornax's FDM halo removes the excited states whose interference generates the fluctuating gravitational field, so soliton oscillation, random-walk motion, and granule evolution all weaken. With no tides, a $10^{-22}$ eV FDM halo drives the stellar half-light radius far beyond the observed value and raises the line-of-sight velocity dispersion above the data; with weak tides the growth is suppressed, and in the strong-tidal realization—Milky Way halo density and Fornax orbital parameters pushed to their $1\sigma$ extremes—the half-light radius falls inside the observed $1\sigma$ band and the velocity dispersion matches the observations. The paper concludes that neglect of tides can produce order-of-magnitude deviations in FDM constraints, and that the same framework can be applied to other dwarfs.

Load-bearing premise

The simulation omits the Milky Way's own fuzzy dark matter wave function; if the host galaxy's granules heat Fornax's stars appreciably, the tidal suppression could be offset and the quantitative conclusion would fail.

Editorial extensions

If this is right

  • A particle mass of $m_a \sim 10^{-22}$ eV becomes compatible with Fornax's size and kinematics, relaxing earlier limits of $m_a \gtrsim 10^{-21}$ eV.
  • No-tidal analyses of satellite heating can overstate FDM constraints by an order of magnitude, so future bounds need tidal histories.
  • Dwarfs sitting closer to the Galactic center, such as Segue 1 and Segue 2, should show even stronger tidal suppression, making previous constraints from them overly stringent.
  • Jeans-based modeling of dwarf galaxies remains valid within roughly 2 kpc even with tides, supporting standard kinematic mass estimates in that regime.
  • Low-mass FDM still faces constraints from other observables such as the subhalo mass function, the Lyman-$\alpha$ forest, and strong lensing.

Reading between the lines

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

  • Beyond the paper: the decisive unknown is the host halo's own FDM wave function; a full-host zoom-in at $10^{-22}$ eV would test whether small host granules reintroduce heating over many orbits.
  • Beyond the paper: applying this framework to a sample of dwarfs with known proper motions could map the viable $m_a$ region against pericenter and host-halo mass, effectively turning satellite heating into a probe of orbital histories.
  • Beyond the paper: because the strong-tidal case strips even inner stars, Fornax may be too tidally disturbed to serve as a clean single-object bound on $m_a$; less disturbed ultra-faint dwarfs would give sharper tests.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. This paper presents a new simulation framework for evolving a fuzzy dark matter (FDM) wave function together with particle-like stars in the rest frame of a satellite dwarf galaxy, subject to a time-dependent tidal potential from a multicomponent Milky Way and the Large Magellanic Cloud. The framework is applied to Fornax for a particle mass of m_a = 10^-22 eV, comparing no-tidal, weak-tidal, and strong-tidal orbital scenarios. The authors find that tidal stripping suppresses FDM-induced heating, so that the strong-tidal simulation yields half-light radii and line-of-sight velocity dispersions within observational uncertainties. The appendices provide the Galactic and LMC potential models, the dynamical friction treatment, a standard derivation of the tidal potential, and the eigenstate-based initialization procedure.

Significance. If the quantitative result holds, the paper would substantially relax lower bounds on m_a derived from Milky Way satellite heating, and it introduces a framework that can be extended to other dwarfs. The qualitative demonstration that tides suppress FDM heating is convincing and is visually clear in the density profiles and velocity dispersion comparisons. The framework is novel in combining a realistic Galactic potential, the LMC, and a self-consistently evolved FDM-stellar system. However, the central quantitative claim currently rests on hand-tuned initial conditions and an unquantified treatment of the Galactic FDM wave function, so the significance depends on the sensitivity analysis requested below.

major comments (3)
  1. [Section 2.3 and Figure 4] The quantitative agreement in the strong-tidal run depends on the three initial-condition parameters M200 = 4.0e8 M_sun, M_star = 5.0e7 M_sun, and R1/2,initial = 0.7 kpc, which are fixed by 'extensive simulation trials' with no reported exploration of the surrounding parameter space. Because the headline claim is that m_a = 10^-22 eV becomes consistent with Fornax, the authors should provide a sensitivity scan over these parameters, include scatter across random initial FDM phases, and compare the chosen values with independent expectations from abundance matching and dwarf-galaxy scaling relations. Without this, the match in Figure 4 may be a selected outcome rather than a robust prediction.
  2. [Section 4] The stated limitation concerning the omitted Galactic FDM wave function is not quantitatively supported. The argument that host-halo granules are smaller than Fornax's granules and that heating efficiency scales with granule volume ignores the dependence of the heating rate on the local density and velocity distribution of the host wave function; smaller but more numerous granules could in principle compensate. A quantitative estimate using the Bar-Or et al. (2019) heating formalism, or a targeted simulation including a host wave function, is needed to verify that host-granule heating is negligible compared with the tidal suppression found here.
  3. [Section 2.1 and Figure 4] The 'strong tidal' scenario is constructed by taking the Galactic halo density parameter and all Fornax orbital parameters to their 1-sigma extremes in the direction that maximizes tidal effects. The pink band in Figure 4 is therefore a bracketing of deterministic extreme choices rather than a statistical uncertainty interval, and the probability of such a conjunction is not quantified. The authors should either weight the halo and orbital parameter choices by their joint likelihood or restrict the central claim to the qualitative statement that tides suppress heating; the current wording overstates the certainty of the quantitative consistency.
minor comments (4)
  1. [Title] The title contains typographical artifacts ('F uzzy' and 'W ay') that should be corrected in the final version.
  2. [Figure 4 caption] The caption states that gray and black points represent Walker et al. (2009) and Breddels & Helmi (2013), respectively, but the text in Section 3 says the strong-tidal simulation matches 'the observational data presented in Breddels & Helmi (2013), as shown by the gray data points.' These attributions are inconsistent and should be reconciled.
  3. [Figure 2 and 3] The stellar density is plotted as a projected 2D density in Figure 2 but as a spherically averaged 3D density in Figure 3, while the color-bar units are not always explicitly distinguished; adding 'projected' or '3D' to the relevant axis labels would avoid ambiguity.
  4. [Figure 1] The 'no LMC' case appears only in the orbital integration and is not included in the simulation suite, so the reader cannot separately assess the LMC's contribution to the suppression; a sentence explaining this choice, or a supplementary simulation, would clarify the role of the LMC.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the tidal-suppression result is established by a controlled no-tidal vs. tidal simulation comparison; self-citations are for numerical methods and are not load-bearing, while the 'extensive simulation trials' initialization is a robustness caveat rather than a circular reduction.

full rationale

The central claim—that Milky Way and LMC tides suppress FDM heating in Fornax—rests on a direct simulation comparison in which the same initial FDM halo and stellar model are evolved under no, weak, and strong tidal potentials. The no-tidal run shows substantial growth of the half-light radius and velocity dispersion, while the tidal runs suppress that growth. Because the no-tidal control uses the identical initial conditions, the suppression is not equivalent to the input by construction; it is a genuine dynamical outcome of the Schrodinger-Poisson evolution with an added external tidal potential. The tidal potential itself is derived from standard mechanics (Appendix C), and the FDM heating mechanism is an external physical process, so there is no self-definitional circularity. The initialization parameters M200, M*, and R1/2,initial are selected 'through extensive simulation trials' to produce a stable and plausible Fornax model, but the paper does not state that they were fitted to the final observed half-light radius or velocity dispersion. The absence of a sensitivity analysis over these parameters is a legitimate robustness concern, but it does not by itself demonstrate that the final comparison is forced by construction. The self-citations to Yang et al. (2025a,b) are for the eigenstate-decomposition initialization and shooting method, which are also attributed to independent work by Yavetz et al. (2022); these numerical-technique citations do not carry the paper's central physical conclusion. The stated omission of the Galactic FDM wave function is a limitation, not a circular input. Overall, the derivation is self-contained and the headline result is an empirically testable simulation prediction, so no significant circularity is found.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the Schrodinger-Poisson description of FDM, an initial equilibrium halo model with a soliton core plus NFW envelope, a Chandrasekhar treatment of dynamical friction, and the assumption that the MW's own FDM wave function is negligible. The free parameters M200, M_star, and R1/2,initial are hand-tuned, and the soliton mass and matching parameter are drawn from stochastic priors. No new particles or forces are introduced.

free parameters (4)
  • FDM halo virial mass M200 = 4.0e8 M_sun
    Adopted through extensive simulation trials (Section 2.3) rather than derived from independent observational constraints; the final agreement with observed stellar properties depends on this choice.
  • Stellar mass M_star = 5.0e7 M_sun
    Chosen through simulation trials (Section 2.3); close to the observed stellar mass of Fornax but not fixed by it in the fitting procedure.
  • Initial 2D half-light radius R1/2,initial = 0.7 kpc
    Chosen through simulation trials (Section 2.3); there is no independent measurement of Fornax's half-light radius 10 Gyr ago, and the final half-light radius is sensitive to this input.
  • Soliton mass Mc and matching parameter k = not reported
    Sampled from Gaussian distributions and selected by maximizing the product of probabilities p1(Mc) and p2(k) (Appendix D); the specific realized values are not given in the paper, which also affects reproducibility.
assumptions (5)
  • standard math FDM is described by the non-relativistic Schrodinger-Poisson system with wave function psi and density m_a |psi|^2.
    Used in Section 2.3, Equation (2), and throughout the simulation; this is the standard effective theory for fuzzy dark matter.
  • domain assumption The initial FDM halo of Fornax is a solitonic core smoothly matched to an NFW envelope.
    Postulated in Appendix D, Equation (D13), motivated by cosmological simulations cited in the paper. The match point and core mass are treated as stochastic parameters.
  • domain assumption Chandrasekhar dynamical friction with b_min = 1 kpc for Fornax and b_min = 4.8 kpc for the LMC is valid.
    Invoked in Appendix B to compute orbits; the paper argues the FDM de Broglie wavelength is small relative to orbital scales, but the choice of b_min for Fornax is not derived from the satellite's physical size.
  • standard math The second-order tidal potential expansion in Equation (1) is accurate for the whole simulation.
    Derived in Appendix C under the assumption that the satellite size is much smaller than the distance to the perturber; this is reasonable for Fornax but not explicitly validated at all times.
  • domain assumption The Galactic FDM wave function does not significantly heat the Fornax stellar system.
    Assumed in Section 4 as a limitation, justified only by a scaling argument about granule volume, without a quantitative calculation for the MW halo at Fornax's orbit.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Tidal Suppression of Fuzzy Dark Matter Heating in Milky Way Satellite Galaxies." pith.science (2026). https://pith.science/paper/J2BNQS3P

@misc{pith2026250701686,
  author       = {Pith},
  title        = {Pith review of: Tidal Suppression of Fuzzy Dark Matter Heating in Milky Way Satellite Galaxies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/J2BNQS3P}},
  note         = {Machine review of arXiv:2507.01686}
}
abstract

Many previous studies have imposed stringent constraints on the particle mass of fuzzy dark matter (FDM) by analyzing observations of Galactic satellite galaxies, which show no significant evidence of the heating effect predicted by FDM. However, these analyses have generally neglected the tidal influence of the Milky Way, which can substantially suppress the FDM-induced heating effect in satellites. This oversight arises from computational challenges of accurately capturing the tidal effects in FDM simulations. In this study, we present a novel simulation framework that, for the first time, enables the simulation of an FDM-stellar system within an observationally motivated gravitational potential of the Milky Way. This framework incorporates the diverse Galactic components, including the gravitational influence of the Large Magellanic Cloud. Using the Fornax dwarf galaxy as a case study, we demonstrate that tidal effects significantly alleviate the tension between observational data and the predicted heating effect for an FDM particle mass of $m_a\sim 10^{-22}$ eV.

Figures

Figures reproduced from arXiv: 2507.01686 by the authors.

Figure 1
Figure 1. Orbital evolution of Fornax. Top and bottom panels show Fornax’s distance to the centers of the MW and the LMC over time, respectively. Green and blue lines rep￾resent the weak and strong tidal cases, respectively. In the top panel, dotted lines illustrate the scenario excluding the influence of the LMC. We conduct simulations for two orbital scenarios cor￾responding to weak and strong tidal effects. In each [PITH_… view at source ↗
Figure 2
Figure 2. Left: 3D FDM density field. These panels show the 3D FDM density distribution, ρFDM(t, x) = ma|ψ(t, x)| 2 , on a plane centered on the solitonic core. The upper-left panel depicts the initial state at t = −10 Gyr, while the remaining panels show the final states under no, weak, and strong tidal conditions, respectively. Right: 2D stellar density field. The panels display stellar density maps obtained via the particl… view at source ↗
Figure 4
Figure 4. Tidal suppression of FDM-induced dynamical heating in Fornax. Vertical dashed lines indicate the 2D half￾light radius. Solid and dotted lines represent the line-of-sight velocity dispersion profiles obtained from simulations and by solving the Jeans equation, respectively. Cyan lines denote the initial state (t = −10 Gyr), while red, green, and blue lines represent the final states (t = 0 Gyr) under conditions of no… view at source ↗
Figures from the paper (1 more)
Figure 3
Figure 3. Figure 3: Left: density profiles of FDM and stars. The solid, dotted, and dashed curves represent the spherically av￾eraged FDM density profiles, the corresponding soliton pro￾files, and the spherically averaged stellar density profiles, re￾spectively. Right: stellar velocity di…

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Updated bounds on ultra-light dark matter from the tiniest galaxies

    astro-ph.CO 2025-09 conditional novelty 6.0 of 10

    If Ursa Major III/UNIONS 1 is a galaxy, ultra-light dark matter particles must be heavier than 8 x 10^-18 eV, the strongest such bound.

Reference graph

Works this paper leans on

66 extracted references · 5 canonical work pages · cited by 1 Pith paper

  1. [1]

    author author D. J. E. \ Marsh \ and\ author J. C. \ Niemeyer ,\ 10.1103/PhysRevLett.123.051103 journal journal Phys. Rev. Lett. \ volume 123 ,\ pages 051103 ( year 2019 ) ,\ http://arxiv.org/abs/1810.08543 arXiv:1810.08543 [astro-ph.CO] NoStop

    arXiv 2019

  2. [2]

    Dalal \ and\ author A

    author author N. Dalal \ and\ author A. Kravtsov ,\ 10.1103/PhysRevD.106.063517 journal journal Phys. Rev. D \ volume 106 ,\ pages 063517 ( year 2022 ) ,\ http://arxiv.org/abs/2203.05750 arXiv:2203.05750 [astro-ph.CO] NoStop

    arXiv 2022

  3. [3]

    Teodori , author A

    author author L. Teodori , author A. Caputo , \ and\ author K. Blum ,\ @noop \ ( year 2025 ) ,\ http://arxiv.org/abs/2501.07631 arXiv:2501.07631 [astro-ph.GA] NoStop

    arXiv 2025

  4. [4]

    Bar-Or , author J.-B

    author author B. Bar-Or , author J.-B. \ Fouvry , \ and\ author S. Tremaine ,\ 10.3847/1538-4357/aaf28c journal journal The Astrophysical Journal \ volume 871 ,\ pages 28 ( year 2019 ) NoStop

    doi:10.3847/1538-4357/aaf28c 2019

  5. [5]

    author author B. V. \ Church , author P. Mocz , \ and\ author J. P. \ Ostriker ,\ 10.1093/mnras/stz534 journal journal Monthly Notices of the Royal Astronomical Society \ volume 485 ,\ pages 2861–2876 ( year 2019 ) NoStop

    doi:10.1093/mnras/stz534 2019

  6. [6]

    author author A. A. \ El-Zant , author Z. Roupas , \ and\ author J. Silk ,\ 10.1093/mnras/staa2972 journal journal Monthly Notices of the Royal Astronomical Society \ volume 499 ,\ pages 2575–2586 ( year 2020 ) NoStop

    work page doi:10.1093/mnras/staa2972 2020

  7. [7]

    author author B. T. \ Chiang , author H.-Y. \ Schive , \ and\ author T. Chiueh ,\ 10.1103/PhysRevD.103.103019 journal journal Phys. Rev. D \ volume 103 ,\ pages 103019 ( year 2021 ) ,\ http://arxiv.org/abs/2104.13359 arXiv:2104.13359 [astro-ph.CO] NoStop

    arXiv 2021

  8. [8]

    author author B. T. \ Chiang , author J. P. \ Ostriker , \ and\ author H.-Y. \ Schive ,\ 10.1093/mnras/stac3358 journal journal Mon. Not. Roy. Astron. Soc. \ volume 518 ,\ pages 4045 ( year 2023 ) ,\ http://arxiv.org/abs/2211.07452 arXiv:2211.07452 [astro-ph.GA] NoStop

    arXiv 2023

Show all 66 references
  1. [9]

    Dutta Chowdhury , author F

    author author D. Dutta Chowdhury , author F. C. \ van den Bosch , author V. H. \ Robles , author P. van Dokkum , author H.-Y. \ Schive , author T. Chiueh , \ and\ author T. Broadhurst ,\ 10.3847/1538-4357/ac043f journal journal The Astrophysical Journal \ volume 916 ,\ pages 2...

    doi

  2. [10]

    Dutta Chowdhury , author F

    author author D. Dutta Chowdhury , author F. C. \ van den Bosch , author P. van Dokkum , author V. H. \ Robles , author H.-Y. \ Schive , \ and\ author T. Chiueh ,\ 10.3847/1538-4357/acc73d journal journal The Astrophysical Journal \ volume 949 ,\ pages 68 ( year 2023 ) NoStop

    doi

  3. [11]

    author author J. F. \ Navarro , author C. S. \ Frenk , \ and\ author S. D. M. \ White ,\ 10.1086/177173 journal journal Astrophys. J. \ volume 462 ,\ pages 563 ( year 1996 ) ,\ http://arxiv.org/abs/astro-ph/9508025 arXiv:astro-ph/9508025 NoStop

    1996 arXiv

  4. [12]

    \ Schive , author T

    author author H.-Y. \ Schive , author T. Chiueh , \ and\ author T. Broadhurst ,\ 10.1103/PhysRevLett.124.201301 journal journal Phys. Rev. Lett. \ volume 124 ,\ pages 201301 ( year 2020 ) ,\ http://arxiv.org/abs/1912.09483 arXiv:1912.09483 [astro-ph.GA] NoStop

    2020 arXiv

  5. [13]

    author author H. Y. J. \ Chan , author H.-Y. \ Schive , author V. H. \ Robles , author A. Kunkel , author G.-M. \ Su , \ and\ author P.-Y. \ Liao ,\ @noop \ ( year 2025 ) ,\ http://arxiv.org/abs/2504.10387 arXiv:2504.10387 [astro-ph.CO] NoStop

    2025 arXiv

  6. [14]

    Widmark , author T

    author author A. Widmark , author T. D. \ Yavetz , \ and\ author X. Li ,\ 10.1088/1475-7516/2024/03/052 journal journal JCAP \ volume 03 ,\ pages 052 ( year 2024 ) ,\ http://arxiv.org/abs/2309.00039 arXiv:2309.00039 [astro-ph.GA] NoStop

    2024 arXiv

  7. [15]

    author author M. Y. \ Wang et al. ( collaboration DES Collaboration ),\ 10.3847/1538-4357/ab31a9 journal journal The Astrophysical Journal \ volume 881 ,\ pages 118 ( year 2019 ) NoStop

    2019 doi

  8. [16]

    author author M. G. \ Walker , author M. Mateo , author E. W. \ Olszewski , author J. Peñarrubia , author N. W. \ Evans , \ and\ author G. Gilmore ,\ 10.1088/0004-637X/704/2/1274 journal journal Astrophys. J. \ volume 704 ,\ pages 1274 ( year 2009 ) ,\ note [Erratum: Astrophys...

    2010 arXiv

  9. [17]

    author author M. A. \ Breddels \ and\ author A. Helmi ,\ 10.1051/0004-6361/201321606 journal journal Astron. Astrophys. \ volume 558 ,\ pages A35 ( year 2013 ) ,\ http://arxiv.org/abs/1304.2976 arXiv:1304.2976 [astro-ph.CO] NoStop

    2013 arXiv

  10. [18]

    author author R. P. \ van der Marel , author D. R. \ Alves , author E. Hardy , \ and\ author N. B. \ Suntzeff ,\ 10.1086/343775 journal journal Astron. J. \ volume 124 ,\ pages 2639 ( year 2002 ) ,\ http://arxiv.org/abs/astro-ph/0205161 arXiv:astro-ph/0205161 NoStop

    2002 arXiv

  11. [19]

    Schönrich , author J

    author author R. Schönrich , author J. Binney , \ and\ author W. Dehnen ,\ 10.1111/j.1365-2966.2010.16253.x journal journal Monthly Notices of the Royal Astronomical Society \ volume 403 ,\ pages 1829–1833 ( year 2010 ) NoStop

    2010

  12. [20]

    Binney \ and\ author S

    author author J. Binney \ and\ author S. Tremaine ,\ http://www.jstor.org/stable/j.ctvc778ff title Galactic Dynamics: Second Edition ,\ edition rev - revised, 2 \ ed.\ ( publisher Princeton University Press ,\ year 2008 ) NoStop

    2008

  13. [21]

    author author A. G. A. \ Brown et al. ( collaboration Gaia Collaboration ),\ 10.1051/0004-6361/202039657e journal journal Astronomy & amp; Astrophysics \ volume 650 ,\ pages C3 ( year 2021 ) NoStop

    2021 doi

  14. [22]

    Battaglia , author S

    author author G. Battaglia , author S. Taibi , author G. F. \ Thomas , \ and\ author T. K. \ Fritz ,\ 10.1051/0004-6361/202141528 journal journal Astronomy & amp; Astrophysics \ volume 657 ,\ pages A54 ( year 2022 ) NoStop

    2022 doi

  15. [23]

    Pietrzyński et al

    author author G. Pietrzyński et al. ,\ 10.1038/s41586-019-0999-4 journal journal Nature \ volume 567 ,\ pages 200–203 ( year 2019 ) NoStop

    2019 doi

  16. [24]

    Battaglia et al

    author author G. Battaglia et al. ,\ 10.1051/0004-6361:20065720 journal journal Astron. Astrophys. \ volume 459 ,\ pages 423 ( year 2006 ) ,\ http://arxiv.org/abs/astro-ph/0608370 arXiv:astro-ph/0608370 NoStop

    2006 arXiv

  17. [25]

    Kallivayalil , author R

    author author N. Kallivayalil , author R. P. \ van der Marel , author G. Besla , author J. Anderson , \ and\ author C. Alcock ,\ 10.1088/0004-637X/764/2/161 journal journal Astrophys. J. \ volume 764 ,\ pages 161 ( year 2013 ) ,\ http://arxiv.org/abs/1301.0832 arXiv:1301.0832 ...

    2013 arXiv

  18. [26]

    author author A. B. \ Pace , author D. Erkal , \ and\ author T. S. \ Li ,\ 10.3847/1538-4357/ac997b journal journal The Astrophysical Journal \ volume 940 ,\ pages 136 ( year 2022 ) NoStop

    2022 doi

  19. [27]

    author author P. J. \ McMillan ,\ 10.1093/mnras/stw2759 journal journal Monthly Notices of the Royal Astronomical Society \ volume 465 ,\ pages 76–94 ( year 2016 ) NoStop

    2016 doi

  20. [28]

    Erkal \ and\ author V

    author author D. Erkal \ and\ author V. A. \ Belokurov ,\ 10.1093/mnras/staa1238 journal journal Monthly Notices of the Royal Astronomical Society \ volume 495 ,\ pages 2554–2563 ( year 2020 ) NoStop

    2020 doi

  21. [29]

    Chandrasekhar ,\ 10.1086/144517 journal journal Astrophys

    author author S. Chandrasekhar ,\ 10.1086/144517 journal journal Astrophys. J. \ volume 97 ,\ pages 255 ( year 1943 ) NoStop

    1943 doi

  22. [30]

    Lancaster , author C

    author author L. Lancaster , author C. Giovanetti , author P. Mocz , author Y. Kahn , author M. Lisanti , \ and\ author D. N. \ Spergel ,\ 10.1088/1475-7516/2020/01/001 journal journal JCAP \ volume 01 ,\ pages 001 ( year 2020 ) ,\ http://arxiv.org/abs/1909.06381 arXiv:1909.06...

    2020 arXiv

  23. [31]

    Hu , author R

    author author W. Hu , author R. Barkana , \ and\ author A. Gruzinov ,\ 10.1103/physrevlett.85.1158 journal journal Physical Review Letters \ volume 85 ,\ pages 1158–1161 ( year 2000 ) NoStop

    doi

  24. [32]

    author author P. J. E. \ Peebles ,\ 10.1086/312677 journal journal Astrophys. J. Lett. \ volume 534 ,\ pages L127 ( year 2000 ) ,\ http://arxiv.org/abs/astro-ph/0002495 arXiv:astro-ph/0002495 NoStop

    arXiv

  25. [33]

    author author D. J. E. \ Marsh ,\ 10.1016/j.physrep.2016.06.005 journal journal Phys. Rept. \ volume 643 ,\ pages 1 ( year 2016 ) ,\ http://arxiv.org/abs/1510.07633 arXiv:1510.07633 [astro-ph.CO] NoStop

    2016 arXiv

  26. [34]

    Hui ,\ 10.1146/annurev-astro-120920-010024 journal journal Ann

    author author L. Hui ,\ 10.1146/annurev-astro-120920-010024 journal journal Ann. Rev. Astron. Astrophys. \ volume 59 ,\ pages 247 ( year 2021 ) ,\ http://arxiv.org/abs/2101.11735 arXiv:2101.11735 [astro-ph.CO] NoStop

    2021 arXiv

  27. [35]

    Hui , author J

    author author L. Hui , author J. P. \ Ostriker , author S. Tremaine , \ and\ author E. Witten ,\ 10.1103/PhysRevD.95.043541 journal journal Phys. Rev. D \ volume 95 ,\ pages 043541 ( year 2017 ) ,\ http://arxiv.org/abs/1610.08297 arXiv:1610.08297 [astro-ph.CO] NoStop

    2017 arXiv

  28. [36]

    author author T. D. \ Yavetz , author X. Li , \ and\ author L. Hui ,\ 10.1103/PhysRevD.105.023512 journal journal Phys. Rev. D \ volume 105 ,\ pages 023512 ( year 2022 ) ,\ http://arxiv.org/abs/2109.06125 arXiv:2109.06125 [astro-ph.CO] NoStop

    2022 arXiv

  29. [37]

    author author Y. M. \ Yang , author X. J. \ Bi , \ and\ author P. F. \ Yin ,\ 10.1103/PhysRevD.111.063013 journal journal Phys. Rev. D \ volume 111 ,\ pages 063013 ( year 2025 a ) ,\ http://arxiv.org/abs/2412.08372 arXiv:2412.08372 [astro-ph.CO] NoStop

    2025 arXiv

  30. [38]

    author author Y. M. \ Yang , author Z. C. \ Zhang , author X. J. \ Bi , \ and\ author P. F. \ Yin ,\ 10.3847/2041-8213/adb7da journal journal Astrophys. J. Lett. \ volume 981 ,\ pages L26 ( year 2025 b ) ,\ http://arxiv.org/abs/2412.01307 arXiv:2412.01307 [astro-ph.GA] NoStop

    2025 arXiv

  31. [39]

    \ Schive , author T

    author author H.-Y. \ Schive , author T. Chiueh , \ and\ author T. Broadhurst ,\ 10.1038/nphys2996 journal journal Nature Phys. \ volume 10 ,\ pages 496 ( year 2014 a ) ,\ http://arxiv.org/abs/1406.6586 arXiv:1406.6586 [astro-ph.GA] NoStop

    2014 arXiv

  32. [40]

    \ Schive , author M.-H

    author author H.-Y. \ Schive , author M.-H. \ Liao , author T.-P. \ Woo , author S.-K. \ Wong , author T. Chiueh , author T. Broadhurst , \ and\ author W. Y. P. \ Hwang ,\ 10.1103/PhysRevLett.113.261302 journal journal Phys. Rev. Lett. \ volume 113 ,\ pages 261302 ( year 2014 ...

    arXiv

  33. [41]

    Veltmaat , author J

    author author J. Veltmaat , author J. C. \ Niemeyer , \ and\ author B. Schwabe ,\ 10.1103/PhysRevD.98.043509 journal journal Phys. Rev. D \ volume 98 ,\ pages 043509 ( year 2018 ) ,\ http://arxiv.org/abs/1804.09647 arXiv:1804.09647 [astro-ph.CO] NoStop

    2018 arXiv

  34. [42]

    \ Liao , author G.-M

    author author P.-Y. \ Liao , author G.-M. \ Su , author H.-Y. \ Schive , author A. Kunkel , author H. Huang , \ and\ author T. Chiueh ,\ @noop \ ( year 2024 ) ,\ http://arxiv.org/abs/2412.09908 arXiv:2412.09908 [astro-ph.CO] NoStop

    2024 arXiv

  35. [43]

    Mocz , author M

    author author P. Mocz , author M. Vogelsberger , author V. H. \ Robles , author J. Zavala , author M. Boylan-Kolchin , author A. Fialkov , \ and\ author L. Hernquist ,\ 10.1093/mnras/stx1887 journal journal Mon. Not. Roy. Astron. Soc. \ volume 471 ,\ pages 4559 ( year 2017 ) ,...

    arXiv

  36. [44]

    Schwabe , author J

    author author B. Schwabe , author J. C. \ Niemeyer , \ and\ author J. F. \ Engels ,\ 10.1103/PhysRevD.94.043513 journal journal Phys. Rev. D \ volume 94 ,\ pages 043513 ( year 2016 ) ,\ http://arxiv.org/abs/1606.05151 arXiv:1606.05151 [astro-ph.CO] NoStop

    2016 arXiv

  37. [45]

    author author H. Y. J. \ Chan , author E. G. M. \ Ferreira , author S. May , author K. Hayashi , \ and\ author M. Chiba ,\ 10.1093/mnras/stac063 journal journal Mon. Not. Roy. Astron. Soc. \ volume 511 ,\ pages 943 ( year 2022 ) ,\ http://arxiv.org/abs/2110.11882 arXiv:2110.11...

    arXiv

  38. [46]

    author author H. H. S. \ Chiu , author H.-Y. \ Schive , author H.-Y. K. \ Yang , author H. Huang , \ and\ author M. Gaspari ,\ 10.1103/PhysRevLett.134.051402 journal journal Phys. Rev. Lett. \ volume 134 ,\ pages 051402 ( year 2025 ) ,\ http://arxiv.org/abs/2501.09098 arXiv:25...

    arXiv

  39. [47]

    Schwabe \ and\ author J

    author author B. Schwabe \ and\ author J. C. \ Niemeyer ,\ 10.1103/PhysRevLett.128.181301 journal journal Phys. Rev. Lett. \ volume 128 ,\ pages 181301 ( year 2022 ) ,\ http://arxiv.org/abs/2110.09145 arXiv:2110.09145 [astro-ph.CO] NoStop

    2022 arXiv

  40. [48]

    author author H. C. \ Plummer ,\ 10.1093/mnras/71.5.460 journal journal Monthly Notices of the Royal Astronomical Society \ volume 71 ,\ pages 460 ( year 1911 ) NoStop

    1911 doi

  41. [49]

    author author A. S. \ Eddington ,\ 10.1093/mnras/76.7.572 journal journal Monthly Notices of the Royal Astronomical Society \ volume 76 ,\ pages 572 ( year 1916 ) NoStop

    1916 doi

  42. [50]

    Edwards , author E

    author author F. Edwards , author E. Kendall , author S. Hotchkiss , \ and\ author R. Easther ,\ 10.1088/1475-7516/2018/10/027 journal journal JCAP \ volume 10 ,\ pages 027 ( year 2018 ) ,\ http://arxiv.org/abs/1807.04037 arXiv:1807.04037 [astro-ph.CO] NoStop

    2018 arXiv

  43. [51]

    Hohl ,\ 10.1086/112259 journal journal Astronomical Journal \ volume 83 ,\ pages 768 ( year 1978 ) NoStop

    author author F. Hohl ,\ 10.1086/112259 journal journal Astronomical Journal \ volume 83 ,\ pages 768 ( year 1978 ) NoStop

    1978 doi

  44. [52]

    Knebe , author A

    author author A. Knebe , author A. Green , \ and\ author J. Binney ,\ 10.1046/j.1365-8711.2001.04532.x journal journal Mon. Not. Roy. Astron. Soc. \ volume 325 ,\ pages 845 ( year 2001 ) ,\ http://arxiv.org/abs/astro-ph/0103503 arXiv:astro-ph/0103503 NoStop

    2001

  45. [53]

    Merz , author U.-L

    author author H. Merz , author U.-L. \ Pen , \ and\ author H. Trac ,\ 10.1016/j.newast.2005.02.001 journal journal New Astron. \ volume 10 ,\ pages 393 ( year 2005 ) ,\ http://arxiv.org/abs/astro-ph/0402443 arXiv:astro-ph/0402443 NoStop

    2005 arXiv

  46. [54]

    Du , author B

    author author X. Du , author B. Schwabe , author J. C. \ Niemeyer , \ and\ author D. B\"urger ,\ 10.1103/PhysRevD.97.063507 journal journal Phys. Rev. D \ volume 97 ,\ pages 063507 ( year 2018 ) ,\ http://arxiv.org/abs/1801.04864 arXiv:1801.04864 [astro-ph.GA] NoStop

    2018 arXiv

  47. [55]

    author author A. W. \ McConnachie ,\ 10.1088/0004-6256/144/1/4 journal journal The Astronomical Journal \ volume 144 ,\ pages 4 ( year 2012 ) NoStop

    2012 doi

  48. [56]

    author author T. J. L. \ de Boer , author E. Tolstoy , author V. Hill , author A. Saha , author E. W. \ Olszewski , author M. Mateo , author E. Starkenburg , author G. Battaglia , \ and\ author M. G. \ Walker ,\ 10.1051/0004-6361/201219547 journal journal Astronomy & amp; Astr...

    doi

  49. [57]

    \ Chen , author H.-Y

    author author S.-R. \ Chen , author H.-Y. \ Schive , \ and\ author T. Chiueh ,\ 10.1093/mnras/stx449 journal journal Mon. Not. Roy. Astron. Soc. \ volume 468 ,\ pages 1338 ( year 2017 ) ,\ http://arxiv.org/abs/1606.09030 arXiv:1606.09030 [astro-ph.GA] NoStop

    2017 arXiv

  50. [58]

    author author H. N. \ Luu , author S. H. H. \ Tye , \ and\ author T. Broadhurst ,\ 10.1016/j.dark.2020.100636 journal journal Phys. Dark Univ. \ volume 30 ,\ pages 100636 ( year 2020 ) ,\ http://arxiv.org/abs/1811.03771 arXiv:1811.03771 [astro-ph.GA] NoStop

    2020

  51. [59]

    Hayashi , author E

    author author K. Hayashi , author E. G. M. \ Ferreira , \ and\ author H. Y. J. \ Chan ,\ 10.3847/2041-8213/abf501 journal journal Astrophys. J. Lett. \ volume 912 ,\ pages L3 ( year 2021 ) ,\ http://arxiv.org/abs/2102.05300 arXiv:2102.05300 [astro-ph.CO] NoStop

    2021 arXiv

  52. [60]

    De Martino ,\ 10.1103/PhysRevD.108.123044 journal journal Phys

    author author I. De Martino ,\ 10.1103/PhysRevD.108.123044 journal journal Phys. Rev. D \ volume 108 ,\ pages 123044 ( year 2023 ) ,\ http://arxiv.org/abs/2312.07217 arXiv:2312.07217 [astro-ph.GA] NoStop

    2023 arXiv

  53. [61]

    Zimmermann , author J

    author author T. Zimmermann , author J. Alvey , author D. J. E. \ Marsh , author M. Fairbairn , \ and\ author J. I. \ Read ,\ 10.1103/PhysRevLett.134.151001 journal journal Phys. Rev. Lett. \ volume 134 ,\ pages 151001 ( year 2025 ) ,\ http://arxiv.org/abs/2405.20374 arXiv:240...

    arXiv

  54. [62]

    Erkal et al

    author author D. Erkal et al. ,\ 10.1093/mnras/stz1371 journal journal Monthly Notices of the Royal Astronomical Society \ volume 487 ,\ pages 2685–2700 ( year 2019 ) NoStop

    2019 doi

  55. [63]

    van der Marel , author P

    author author R. van der Marel , author P. , \ and\ author N. Kallivayalil ,\ 10.1088/0004-637X/781/2/121 journal journal Astrophys. J. \ volume 781 ,\ pages 121 ( year 2014 ) ,\ http://arxiv.org/abs/1305.4641 arXiv:1305.4641 [astro-ph.CO] NoStop

    2014 arXiv

  56. [64]

    author author A. R. \ Zentner \ and\ author J. S. \ Bullock ,\ 10.1086/378797 journal journal Astrophys. J. \ volume 598 ,\ pages 49 ( year 2003 ) ,\ http://arxiv.org/abs/astro-ph/0304292 arXiv:astro-ph/0304292 NoStop

    2003 arXiv

  57. [65]

    Besla et al

    author author G. Besla et al. ,\ 10.1086/521385 journal journal Astrophys. J. \ volume 668 ,\ pages 949 ( year 2007 ) ,\ http://arxiv.org/abs/astro-ph/0703196 arXiv:astro-ph/0703196 NoStop

    2007 arXiv

  58. [66]

    author author A. D. \ Ludlow et al. ,\ 10.1093/mnras/stw1046 journal journal Mon. Not. Roy. Astron. Soc. \ volume 460 ,\ pages 1214 ( year 2016 ) ,\ http://arxiv.org/abs/1601.02624 arXiv:1601.02624 [astro-ph.CO] NoStop

    2016 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.