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Fuzzy dark matter mass from eight dwarf spheroidals is bimodal: a ~1e-20 eV branch and a ~1e-22 eV branch that appears only when core-halo scatter is included.

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2026-08-03 02:32 UTC pith:H57BAY54

load-bearing objection The low-mass FDM window is interesting but rests on an ad hoc CHR ensemble; the paper needs a same-pipeline baseline before that claim is taken seriously. the 4 major comments →

arxiv 2603.07175 v3 pith:H57BAY54 submitted 2026-03-07 astro-ph.GA

Fuzzy Dark Matter and the Impact of Core--Halo Diversity on Its Particle Mass Constraints

Dafa Wardana , Kohei Hayashi , Masashi Chiba , Elisa G. M. Ferreira This is my paper
classification astro-ph.GA
keywords fuzzy dark mattersoliton corecore-halo mass relationdwarf spheroidal galaxiesstellar kinematicsJeans analysisfourth-order velocity momentskurtosis
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper re-derives the fuzzy dark matter particle mass from stellar kinematics of eight Milky Way dwarf spheroidals, allowing the core-halo mass relation to scatter as in cosmological simulations and adding fourth-order velocity moments. It finds two allowed mass windows: a high-mass near 1e-20 eV and a low-mass near 1e-22 eV that emerges only with core-halo diversity. The low-mass window corresponds to large soliton cores enclosing most tracer stars; the high-mass to compact cores with a steep transition outside the data. The authors conclude that earlier one-to-one core-halo constraints were artificially restrictive.

Core claim

The paper claims that the fuzzy dark matter particle mass inferred from eight dwarf spheroidals is bimodal. Combining posteriors yields log10(m_psi/eV) = -21.82 (+0.35/-0.26) and -19.79 (+0.60/-0.53) at 68% credible intervals. The low-mass window becomes prominent only when the core-halo mass relation is treated as an ensemble of 500 realizations within the scatter of simulations. The two solutions arise because the soliton density profile falls steeply (rho ~ r^-16) beyond the core radius, so the model avoids configurations where many stars sit in the transition region. The paper argues that one-to-one core-halo constraints were artificially restrictive.

What carries the argument

The analysis uses a two-component halo model: a soliton core embedded in an NFW envelope, matched at a transition radius. The core-halo relation is represented by 500 realizations of its parameters drawn uniformly within simulation scatter. Stellar kinematics are modeled with Jeans equations through fourth order, using kurtosis to break the mass-anisotropy degeneracy. The steep soliton falloff creates the two configurations, and the core-halo scatter lets the small-mass window survive.

Load-bearing premise

The low-mass window relies on treating 500 core-halo realizations, drawn uniformly within the scatter band of existing simulations, as an equal-weight ensemble; if the true distribution of halo properties is non-uniform or narrower, the low-mass solution may be an artifact.

What would settle it

Recompute the posterior with a fully probabilistic, empirically weighted core-halo relation from a larger simulation suite; if the low-mass peak disappears or the 68% interval no longer includes log10(m_psi/eV) around -21.8, the central claim fails. Alternatively, a dwarf spheroidal with kinematic tracers extending well beyond its half-light radius and a steeply falling velocity dispersion without a large flat core would rule out the low-mass branch.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Earlier constraints from one-to-one core-halo relations are not robust; including scatter opens a lower mass window around 1e-22 eV.
  • The high-mass window near 1e-20 eV remains broadly compatible with other astrophysical bounds, while the low-mass window is closer to the edge of some constraints.
  • The bimodality is a statistical feature, not evidence of two physical populations; future data are needed to decide.
  • Fourth-order velocity moments sharpen the separation, showing kurtosis carries real constraining power.
  • Extending stellar samples beyond current radial coverage should distinguish the branches because the low-mass branch requires a core radius large enough to enclose most tracers.

Where Pith is reading between the lines

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

  • Beyond the paper: if the true core-halo scatter is non-uniform or narrower, the low-mass window could shift or vanish; a fully probabilistic treatment would test this.
  • Applying the same ensemble to ultrafaint dwarfs would either sharpen or resolve the tension with dwarf spheroidals.
  • The correlation between inferred core radius and median stellar radius suggests selecting dwarfs with the most extended stellar distributions to exclude the large-core branch.
  • Quoting a single fuzzy dark matter mass from a single core-halo relation may be misleading; constraints should be reported as a function of the assumed scatter.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper infers the fuzzy dark matter particle mass m_ψ from the line-of-sight kinematics of eight Milky Way dwarf spheroidals. The halo model is a soliton core matched to an NFW envelope, and the analysis uses both second- and fourth-order Jeans equations with unbinned, kernel-based likelihoods. The distinctive new ingredient is an ensemble of N_CHR = 500 realizations of the generalized core–halo mass relation of Chan et al. (2022), intended to capture intrinsic scatter in the Mc–M200 relation. The main result is a bimodal posterior for m_ψ, with log10(m_ψ/eV) ≈ -21.8 and ≈ -19.8 at 68% credibility, and the claim that the low-mass window appears only when core–halo diversity is included. The paper also compiles and compares against external constraints from CMB, Lyman-α, superradiance, satellite abundances, and stellar-stream/UFD heating analyses.

Significance. If the central claim is correct, it would substantially alter the interpretation of dwarf-galaxy kinematic constraints on FDM: it would show that previously reported lower bounds based on a one-to-one Schive et al. (2014) CHR are artificially restrictive, and that a second, lower-mass window around 10^-21.8 eV remains consistent with dSph kinematics once realistic CHR scatter is included. The paper is careful in several respects: it uses unbinned stellar velocities (avoiding binning information loss), includes fourth-order velocity moments through kurtosis with flexible kernels, and explicitly discusses systematic modeling uncertainties and external probes. The methodology is standard and the numerical machinery appears straightforward. However, the paper's new physical conclusion depends entirely on how the CHR ensemble is constructed and weighted, and that construction is not currently demonstrated to be robust. The comparison with previous work is also not controlled, so the attribution of the low-mass window to CHR diversity rather than to the simultaneous introduction of fourth-order moments is not established.

major comments (4)
  1. [§2.2, Eqs. (12)–(14)] The load-bearing ingredient is the N_CHR = 500 ensemble of (ξ, μ, η) realizations, drawn to 'uniformly populate the log10(Mc)–log10(M200) plane within the scatter reported by Chan et al. (2022)' and then used as an equal-weight ensemble. This is not a posterior marginalization over the true CHR distribution. Uniform sampling over the quoted asymmetric intervals overweights tails and underweights the correlated region where most simulated halos reside; the manuscript itself concedes that a fully probabilistic treatment would be more realistic but does not implement one. Because the low-mass peak appears only under this ensemble, the central claim is not yet robust. Please provide sensitivity tests: e.g., Gaussian or log-normal weighting of the Chan et al. scatter, varying N_CHR, expanding/contracting the scatter, and a hierarchical treatment that samples CHR parameters jointly with the ot
  2. [§5, Hayashi et al. (2021) comparison] The paper states that including CHR diversity 'leads to a qualitatively different posterior structure' and that the low-mass window becomes prominent only with CHR diversity. The only quantitative comparison offered is with Hayashi et al. (2021), which differs in two major respects: it uses a one-to-one Schive CHR and only second-order velocity moments. The present paper also introduces fourth-order moments and kernel-based likelihoods. Without a same-pipeline baseline that fixes the Schive CHR while keeping the fourth-order moments, unbinned likelihood, data set, and priors identical, the attribution to CHR diversity is not demonstrated. Please run and report the fixed-CHR control case under the same code, or explicitly separate the effects of the two changes.
  3. [Eqs. (16)–(17), §3] The concentration–mass likelihood used for log10(L_c200) depends on the subhalo position parameter x_sub through Eq. (16), yet x_sub is not listed among the free parameters, given a prior, or specified as a fixed value. Because M200 is a free parameter and M200 enters the CHR in Eq. (12), this unspecified input can affect which m_ψ windows are allowed. Please state the assumed value/distribution of x_sub and test sensitivity to it; also justify the adopted σ_c200 = 0.13.
  4. [Abstract vs. §4/§6] The abstract reports log10(m_ψ/eV) = -19.72^{+0.64}_{-0.56} and -21.81^{+0.39}_{-0.26}, while Section 4 and Section 6 report -19.79^{+0.60}_{-0.53} and -21.82^{+0.35}_{-0.26}. These are quoted as the same 68% credible intervals but differ. Please correct the inconsistency and ensure all quoted intervals correspond to the same posterior definition.
minor comments (5)
  1. [Eq. (14)] The kernel function fs(w) is used in the likelihood but never defined. Please give the explicit normalized uniform and Laplacian forms and state the criterion for choosing between them (κlos < 3 vs > 3) precisely, including how the transition is handled when κlos is close to 3.
  2. [§3, parameter list] The text says 'the full model contains five free parameters' but does not list the CHR parameters (ξ, μ, η) among them. Clarify whether each MCMC run uses a fixed CHR realization, whether the likelihood is averaged over the 500 realizations, or whether CHR parameters are sampled hierarchically. This is essential for reproducibility.
  3. [§3, MCMC convergence] Convergence is assessed only by visual inspection. Please provide quantitative convergence diagnostics (e.g., Gelman–Rubin R-hat or effective sample size) for the reported posteriors, especially since the posterior is multimodal and the chains are short (5000 samples, 2000 burn-in).
  4. [§5, combined posterior] The statement that the combined constraints are derived by 'directly combining' the eight individual posteriors is vague. Specify whether this is a product of likelihoods, a union of credible intervals, or another procedure, since this affects the meaning of the final ranges.
  5. [General] There are minor typographical issues, e.g., 'Navaro–Frenk–White' in Section 2 and 's implyc' in Section 2. Also, the color coding in Figure 3 is described in the caption but no color bar is visible in the provided text; please ensure the figure is legible in the final version.

Circularity Check

0 steps flagged

No circularity: the inference is conditioned on external simulation-calibrated inputs, and the CHR ensemble is an acknowledged prior choice, not a fitted prediction.

full rationale

The derivation chain is not circular. The soliton profile, core–soliton scaling, generalized core–halo relation, and concentration–mass relation are imported from external simulations and empirical fits (Schive et al. 2014a,b; Chan et al. 2022; Moliné et al. 2017), not derived from the dSph kinematics being analyzed. The posterior for mψ is obtained from unbinned stellar velocity data through the Jeans equations, so the kinematic data carry independent information. The N_CHR=500 realization ensemble is a fixed equal-weight prior motivated by CHR scatter; the paper explicitly concedes that 'a fully probabilistic treatment of the core–halo mass distribution would be more realistic' but uses the uniform ensemble because of limited simulated halos. This is a sensitivity/prior-robustness limitation, not a hidden fit: the CHR parameters are not adjusted to the stellar data, and the low-mass window is not equivalent by construction to the prior, since it emerges only through the likelihood evaluated against the kinematics. The self-citations to Chan et al. (2022) and Wardana et al. (2025) provide external, simulation/standard-method support rather than an unverified uniqueness claim. No equation reduces to another by definition, and no fitted parameter is renamed as a prediction. Therefore no specific circular step can be exhibited.

Axiom & Free-Parameter Ledger

7 free parameters · 9 axioms · 0 invented entities

The inference rests on standard Jeans modeling plus an empirical soliton/NFW halo description from the literature. The main non-standard ingredient is a hand-built ensemble of 500 CHR realizations drawn from the scatter of Chan et al. (2022); no new particle, force, or conserved quantity is introduced. All five physical parameters of the halo model are fit to the kinematic data, so the posterior windows are fit outputs, not predictions.

free parameters (7)
  • β (velocity anisotropy) = Table 2, e.g. -log10(1-β) ≈ -0.14 to 0.15
    Free parameter per galaxy, marginalized over log-flat prior.
  • mψ (FDM particle mass) = Bimodal posterior, Table 2
    Primary target; free parameter per galaxy.
  • M200 (halo mass) = log10(M200/Msun) ≈ 8.5-9.4, Table 2
    Free parameter per galaxy, enters CHR and NFW envelope.
  • ϵ (transition density ratio) = rt/rc ≈ 2.6-3.3, Table 2
    Free parameter controlling soliton-to-NFW transition radius.
  • rs (NFW scale radius) = log10(rs/kpc) ≈ -0.1 to 0.3, Table 2
    Free parameter per galaxy.
  • CHR parameters (ξ, μ, η) = ξ=8.00e6 Msun, log10(μ/Msun)=-5.73, η=0.515 (from Chan et al. 2022)
    Adopted from simulations; 500 realizations are drawn across their scatter and treated as a uniform ensemble.
  • N_CHR (number of CHR realizations) = 500
    Chosen by hand to ensure 'smooth' sampling; no convergence or seed check is shown.
axioms (9)
  • domain assumption Dynamical equilibrium and spherical symmetry for dSph stellar systems
    Stated in Section 2 and again in Section 5; the Jeans equations require these assumptions.
  • domain assumption Constant stellar velocity anisotropy, β(r)=β
    Invoked to close the Jeans equations and project moments; Section 2.
  • domain assumption Plummer stellar density profile
    Adopted for all eight dwarfs; Section 2, Eq. (3) context.
  • domain assumption Empirical soliton profile of Schive et al., Eq. (7), accurately describes FDM halo centers
    Basis for connecting density to mψ via Eq. (8); Section 2.1.
  • domain assumption Soliton and NFW components are matched by density continuity only at rt
    The paper notes a smoother matching may alter inferred mψ constraints; Section 2.1 and footnote 6.
  • domain assumption The CDM subhalo concentration–mass relation, Eq. (16), applies to FDM halos
    The paper asserts the FDM-CDM difference is negligible but provides no quantitative demonstration; Section 3.
  • domain assumption Binary stars contribute negligibly to the velocity dispersion of the selected dSphs
    Assumed in Section 3; justifies use of stars as collisionless tracers.
  • ad hoc to paper Uniform sampling of N_CHR=500 CHR realizations is an adequate representation of core–halo diversity
    This is the paper's central methodological innovation but is ad hoc; the authors state a fully probabilistic treatment would be more realistic.
  • domain assumption The soliton core is stationary and centered on the galaxy
    Acknowledged in Section 5: stochastic core motion is not accounted for.

pith-pipeline@v1.3.0-alltime-deepseek · 20187 in / 12798 out tokens · 132148 ms · 2026-08-03T02:32:20.382646+00:00 · methodology

0 comments
read the original abstract

We investigate how diversity in the core--halo mass relation and the inclusion of higher-order velocity moments affect constraints on the fuzzy dark matter particle mass ($m_\psi$) inferred from the internal kinematics of dwarf galaxies. Using stellar line-of-sight velocities and projected positions for eight Milky Way dwarf spheroidal galaxies, we model their dark matter halos as solitonic cores embedded within outer Navarro--Frenk--White envelopes. We apply both second- and fourth-order Jeans analyses to derive the posterior distribution of $m_\psi$. Our results show that there are two ranges of $m_\psi$ consistent with the observed kinematics: $\log_{10}(m_\psi/\mathrm{eV}) = -19.72^{+0.64}_{-0.56}$, and a narrower low-mass window $\log_{10}(m_\psi/\mathrm{eV}) = -21.81^{+0.39}_{-0.26}$, both within the 68\% credible intervals. The latter becomes prominent only when core--halo diversity is taken into account, which highlights the sensitivity of the inferred fuzzy dark matter particle mass constraints to our understanding of the core--halo relation. Future observations, providing larger stellar samples and more precise kinematic measurements, will be essential for clarifying the allowed parameter space of fuzzy dark matter.

Figures

Figures reproduced from arXiv: 2603.07175 by Dafa Wardana, Elisa G. M. Ferreira, Kohei Hayashi, Masashi Chiba.

Figure 1
Figure 1. Figure 1: presents the inferred values of mψ for each analyzed dSph with thick and thin error bars indicating the 68% and 95% credible intervals, respectively. All galaxies exhibit a bimodal posterior distribution in mψ, [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Core radius rc of the small-mψ solutions as a function of the median projected galactocentric distance of the kinematic samples. Error bars denote the 68% credible intervals. The solid gray line represents rc = median(R) to guide the readers. For the small-mψ solution, the dark mat￾ter (DM) core radius must be sufficiently large to encompass most of the kinematic tracers within the core region, which gives… view at source ↗
Figure 3
Figure 3. Figure 3: Upper panel: MCMC samples of the estimated log10(M200) versus log10(mψ/eV) for Draco as representa￾tive. The colors are coded based on the slope of the CHR η. Lower panel: similar to the upper panel but for rt/rc versus log10(mψ/eV) with the colors coded by log10(rs/kpc). allowed range of mψ becomes restricted to the small￾mψ solutions because other ranges will place many kine￾matic samples in the fast dec… view at source ↗
Figure 4
Figure 4. Figure 4: Constraints on the fuzzy dark matter particle mass. Points with error bars indicate the ranges of mψ consistent with the data within the 68% (thick error bars) and 95% (thin error bars) credible intervals. Shaded bands denote excluded ranges of mψ. The upper section, in cyan and brown, shows constraints derived from this work and from other kinematic analyses of dwarf galaxies, respectively. Darker and lig… view at source ↗
Figure 5
Figure 5. Figure 5: The posterior distributions of the model parameters for Carina, Draco, Fornax, and Leo I. Although rc is not treated as a free parameter in the model, it is included here for reference [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The same as [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The left and right panels show the recovered LOS velocity dispersion and LOS kurtosis profiles of the Draco dSph, respectively. The darker and lighter shaded bands indicate the 68% and 95% credible intervals, with green and orange corre￾sponding to the small- and large-mψ solutions. Purple curves show the predicted σlos and κlos profiles for log10(mψ/eV) = −21.4. The different line thicknesses correspond t… view at source ↗

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Forward citations

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Works this paper leans on

84 extracted references · 12 canonical work pages · cited by 3 Pith papers

  1. [1]

    Ando, S., Ferreira, E. G. M., & Horigome, S. 2026,

    2026

  2. [2]

    M., Battaglia, G., Thomas, G

    Arroyo-Polonio, J. M., Battaglia, G., Thomas, G. F., et al. 2023, A&A, 677, A95, doi: 10.1051/0004-6361/202346843 Bañares-Hernández, A., Read, J. I., & Júlio, M. P. 2025, arXiv e-prints, arXiv:2509.24103, doi: 10.48550/arXiv.2509.24103

    Pith/arXiv arXiv doi:10.48550/arxiv.2509.24103 2023

  3. [3]

    Banik, N., Bovy, J., Bertone, G., Erkal, D., & de Boer, T. J. L. 2021, JCAP, 2021, 043, doi: 10.1088/1475-7516/2021/10/043

    doi:10.1088/1475-7516/2021/10/043 2021

  4. [4]

    2013, NewAR, 57, 52, doi: 10.1016/j.newar.2013.05.003

    Battaglia, G., Helmi, A., & Breddels, M. 2013, NewAR, 57, 52, doi: 10.1016/j.newar.2013.05.003

    work page doi:10.1016/j.newar.2013.05.003 2013

  5. [5]

    2022, Nature Astronomy, 6, 659, doi: 10.1038/s41550-022-01638-7

    Battaglia, G., & Nipoti, C. 2022, Nature Astronomy, 6, 659, doi: 10.1038/s41550-022-01638-7

    doi:10.1038/s41550-022-01638-7 2022

  6. [6]

    Bellazzini, M., Gennari, N., & Ferraro, F. R. 2005, MNRAS, 360, 185, doi: 10.1111/j.1365-2966.2005.09027.x

    arXiv 2005

  7. [7]

    R., & Sollima, A

    Bellazzini, M., Gennari, N., Ferraro, F. R., & Sollima, A. 2004, Monthly Notices of the Royal Astronomical Society, 354, 708, doi: 10.1111/j.1365-2966.2004.08226.x

    arXiv 2004

  8. [8]

    C., Hütsi, G., Raidal, M., & Veermäe, H

    Benito, M., Criado, J. C., Hütsi, G., Raidal, M., & Veermäe, H. 2020, PhRvD, 101, 103023, doi: 10.1103/PhysRevD.101.103023

    doi:10.1103/physrevd.101.103023 2020

  9. [9]

    1998, Galactic Astronomy (Princeton University Press)

    Binney, J., & Merrifield, M. 1998, Galactic Astronomy (Princeton University Press)

    1998

  10. [10]

    2008, Galactic Dynamics: Second Edition (Princeton University Press)

    Binney, J., & Tremaine, S. 2008, Galactic Dynamics: Second Edition (Princeton University Press)

    2008

  11. [11]

    D., & Bakos, G

    Sasselov, D. D., & Bakos, G. Á. 2004, The Astronomical Journal, 127, 861, doi: 10.1086/381073

    work page doi:10.1086/381073 2004

  12. [12]

    S., & Boylan-Kolchin, M

    Bullock, J. S., & Boylan-Kolchin, M. 2017, Annual Review of Astronomy and Astrophysics, 55, 343, doi: 10.1146/annurev-astro-091916-055313

    doi:10.1146/annurev-astro-091916-055313 2017

  13. [13]

    2002, The Astronomical Journal, 123, 3199, doi: 10.1086/340702

    Carrera, R., Aparicio, A., Martínez-Delgado, D., & Alonso-García, J. 2002, The Astronomical Journal, 123, 3199, doi: 10.1086/340702

    doi:10.1086/340702 2002

  14. [14]

    2022, MNRAS, 511, 943, doi: 10.1093/mnras/stac063

    Chiba, M. 2022, MNRAS, 511, 943, doi: 10.1093/mnras/stac063

    doi:10.1093/mnras/stac063 2022

  15. [15]

    2017, MNRAS, 468, 1338, doi: 10.1093/mnras/stx449

    Chen, S.-R., Schive, H.-Y., & Chiueh, T. 2017, MNRAS, 468, 1338, doi: 10.1093/mnras/stx449

    doi:10.1093/mnras/stx449 2017

  16. [16]

    2022, Physical Review D, 106, 063517, doi: 10.1103/PhysRevD.106.063517

    Dalal, N., & Kravtsov, A. 2022, Physical Review D, 106, 063517, doi: 10.1103/PhysRevD.106.063517

    doi:10.1103/physrevd.106.063517 2022

  17. [17]

    Davoudiasl, H., & Denton, P. B. 2019, PhRvL, 123, 021102, doi: 10.1103/PhysRevLett.123.021102 de Martino, I. 2023, PhRvD, 108, 123044, doi: 10.1103/PhysRevD.108.123044 Dutta Chowdhury, D., van den Bosch, F. C., Robles, V. H., et al. 2021, ApJ, 916, 27, doi: 10.3847/1538-4357/ac043f

    work page doi:10.1103/physrevlett.123.021102 2019

  18. [18]

    Eberhardt, A., & Ferreira, E. G. M. 2025, arXiv e-prints, arXiv:2507.00705, doi: 10.48550/arXiv.2507.00705

    Pith/arXiv arXiv doi:10.48550/arxiv.2507.00705 2025

  19. [19]

    2025, arXiv e-prints, arXiv:2510.17079, doi: 10.48550/arXiv.2510.17079 13 Figure 5.The posterior distributions of the model parameters for Carina, Draco, Fornax, and Leo I

    Eberhardt, A., Gosenca, M., & Hui, L. 2025, arXiv e-prints, arXiv:2510.17079, doi: 10.48550/arXiv.2510.17079 13 Figure 5.The posterior distributions of the model parameters for Carina, Draco, Fornax, and Leo I. Althoughrc is not treated as a free parameter in the model, it is included here for reference. 14 Figure 6.The same as Figure 5, but for Leo II, S...

    doi:10.48550/arxiv.2510.17079 2025

  20. [20]

    2016, The Astrophysical Journal, 830, 126, doi: 10.3847/0004-637X/830/2/126

    Fabrizio, M., Bono, G., Nonino, M., et al. 2016, The Astrophysical Journal, 830, 126, doi: 10.3847/0004-637X/830/2/126

    work page doi:10.3847/0004-637x/830/2/126 2016

  21. [21]

    Ferreira, E. G. M. 2021, Astronomy & Astrophysics Review, 29, 7, doi: 10.1007/s00159-021-00135-6

    doi:10.1007/s00159-021-00135-6 2021

  22. [22]

    I., Frenk, C

    Genina, A., Read, J. I., Frenk, C. S., et al. 2020, MNRAS, 498, 144, doi: 10.1093/mnras/staa2352

    doi:10.1093/mnras/staa2352 2020

  23. [23]

    S., Koushiappas, S

    Goldstein, I. S., Koushiappas, S. M., & Walker, M. G. 2022, PhRvD, 106, 063010, doi: 10.1103/PhysRevD.106.063010 González-Morales, A. X., Marsh, D. J. E., Peñarrubia, J., & Ureña-López, L. A. 2017, MNRAS, 472, 1346, doi: 10.1093/mnras/stx1941

    work page doi:10.1103/physrevd.106.063010 2022

  24. [24]

    Hastings, W. K. 1970, Biometrika, 57, 97, doi: 10.1093/biomet/57.1.97

    doi:10.1093/biomet/57.1.97 1970

  25. [25]

    Hayashi, K., Ferreira, E. G. M., & Chan, H. Y. J. 2021, ApJL, 912, L3, doi: 10.3847/2041-8213/abf501

    doi:10.3847/2041-8213/abf501 2021

  26. [26]

    2020, MNRAS, 491, 615, doi: 10.1093/mnras/stz2950 Hložek, R., Marsh, D

    Hayashi, K., & Obata, I. 2020, MNRAS, 491, 615, doi: 10.1093/mnras/stz2950 Hložek, R., Marsh, D. J. E., & Grin, D. 2018, Monthly Notices of the Royal Astronomical Society, 476, 3063, doi: 10.1093/mnras/sty271

    work page doi:10.1093/mnras/stz2950 2020

  27. [27]

    Hlozek, R., Grin, D., Marsh, D. J. E., & Ferreira, P. G. 2015, Physical Review D, 91, 103512, doi: 10.1103/PhysRevD.91.103512

    doi:10.1103/physrevd.91.103512 2015

  28. [28]

    2000, Physical Review Letters, 85, 1158, doi: 10.1103/PhysRevLett.85.1158

    Hu, W., Barkana, R., & Gruzinov, A. 2000, Physical Review Letters, 85, 1158, doi: 10.1103/PhysRevLett.85.1158

    doi:10.1103/physrevlett.85.1158 2000

  29. [29]

    2021, ARA&A, 59, 247, doi: 10.1146/annurev-astro-120920-010024

    Hui, L. 2021, ARA&A, 59, 247, doi: 10.1146/annurev-astro-120920-010024

    doi:10.1146/annurev-astro-120920-010024 2021

  30. [30]

    P., Tremaine, S., & Witten, E

    Hui, L., Ostriker, J. P., Tremaine, S., & Witten, E. 2017, PhRvD, 95, 043541, doi: 10.1103/PhysRevD.95.043541

    doi:10.1103/physrevd.95.043541 2017

  31. [31]

    Hunter, J. D. 2007, Computing in Science and Engineering, 9, 90, doi: 10.1109/MCSE.2007.55 Iršič, V., Viel, M., Haehnelt, M. G., Bolton, J. S., &

    doi:10.1109/mcse.2007.55 2007

  32. [32]

    Becker, G. D. 2017, PhRvL, 119, 031302, doi: 10.1103/PhysRevLett.119.031302

    doi:10.1103/physrevlett.119.031302 2017

  33. [33]

    A., et al

    Ishiyama, T., Prada, F., Klypin, A. A., et al. 2021, MNRAS, 506, 4210, doi: 10.1093/mnras/stab1755

    doi:10.1093/mnras/stab1755 2021

  34. [34]

    2024, PhRvD, 110, 023519, doi: 10.1103/PhysRevD.110.023519

    Kawai, H., Kamada, A., Kamada, K., & Yoshida, N. 2024, PhRvD, 110, 023519, doi: 10.1103/PhysRevD.110.023519

    doi:10.1103/physrevd.110.023519 2024

  35. [35]

    N., Boylan-Kolchin, M., Cohen, J

    Kirby, E. N., Boylan-Kolchin, M., Cohen, J. G., et al. 2013, ApJ, 770, 16, doi: 10.1088/0004-637X/770/1/16

    doi:10.1088/0004-637x/770/1/16 2013

  36. [36]

    N., Cohen, J

    Kirby, E. N., Cohen, J. G., Simon, J. D., et al. 2017, ApJ, 838, 83, doi: 10.3847/1538-4357/aa6570

    doi:10.3847/1538-4357/aa6570 2017

  37. [37]

    T., Wilkinson, M

    Koch, A., Kleyna, J. T., Wilkinson, M. I., et al. 2007, The Astronomical Journal, 134, 566, doi: 10.1086/519380

    work page doi:10.1086/519380 2007

  38. [38]

    2022, MNRAS, 517, 1867, doi: 10.1093/mnras/stac2677

    Laroche, A., Gilman, D., Li, X., Bovy, J., & Du, X. 2022, MNRAS, 517, 1867, doi: 10.1093/mnras/stac2677

    doi:10.1093/mnras/stac2677 2022

  39. [39]

    G., Yuk, I.-S., Park, H

    Lee, M. G., Yuk, I.-S., Park, H. S., Harris, J., & Zaritsky, D. 2009, The Astrophysical Journal, 703, 692, doi: 10.1088/0004-637X/703/1/692

    work page doi:10.1088/0004-637x/703/1/692 2009

  40. [40]

    2025, PhRvL, 135, 061002, doi: 10.1103/9dqj-q6mt Łokas, E

    Liao, P.-Y., Su, G.-M., Schive, H.-Y., et al. 2025, PhRvL, 135, 061002, doi: 10.1103/9dqj-q6mt Łokas, E. L. 2002, MNRAS, 333, 697, doi: 10.1046/j.1365-8711.2002.05457.x Macciò, A. V., Paduroiu, S., Anderhalden, D., Schneider, A., & Moore, B. 2012, MNRAS, 424, 1105, doi: 10.1111/j.1365-2966.2012.21284.x María Arroyo-Polonio, J., Battaglia, G., & Thomas, G....

    arXiv 2025

  41. [41]

    Marsh, D. J. E., & Niemeyer, J. C. 2019, PhRvL, 123, 051103, doi: 10.1103/PhysRevLett.123.051103

    doi:10.1103/physrevlett.123.051103 2019

  42. [42]

    W., & Walker, M

    Mateo, M., Olszewski, E. W., & Walker, M. G. 2008, The Astrophysical Journal, 675, 201, doi: 10.1086/522326

    doi:10.1086/522326 2008

  43. [43]

    2025, arXiv e-prints, arXiv:2509.02781, doi: 10.48550/arXiv.2509.02781

    May, S., Dalal, N., & Kravtsov, A. 2025, arXiv e-prints, arXiv:2509.02781, doi: 10.48550/arXiv.2509.02781

    Pith/arXiv arXiv doi:10.48550/arxiv.2509.02781 2025

  44. [44]

    2021, MNRAS, 506, 2603, doi: 10.1093/mnras/stab1764

    May, S., & Springel, V. 2021, MNRAS, 506, 2603, doi: 10.1093/mnras/stab1764

    doi:10.1093/mnras/stab1764 2021

  45. [45]

    McConnachie, A. W. 2012, The Astronomical Journal, 144, 4, doi: 10.1088/0004-6256/144/1/4

    doi:10.1088/0004-6256/144/1/4 2012

  46. [46]

    W., & Côté, P

    McConnachie, A. W., & Côté, P. 2010, ApJL, 722, L209, doi: 10.1088/2041-8205/722/2/L209

    doi:10.1088/2041-8205/722/2/l209 2010

  47. [47]

    R., & Kent, S

    Merrifield, M. R., & Kent, S. M. 1990, in Bulletin of the American Astronomical Society, Vol. 22, 744

    1990

  48. [48]

    H., & Teller, E

    Teller, A. H., & Teller, E. 1953, JChPh, 21, 1087, doi: 10.1063/1.1699114

    doi:10.1063/1.1699114 1953

  49. [49]

    F., & Winther, H

    Mina, M., Mota, D. F., & Winther, H. A. 2022, A&A, 662, A29, doi: 10.1051/0004-6361/202038876

    work page doi:10.1051/0004-6361/202038876 2022

  50. [50]

    Minor, Q. E. 2013, ApJ, 779, 116, doi: 10.1088/0004-637X/779/2/116

    doi:10.1088/0004-637x/779/2/116 2013

  51. [51]

    H., et al

    Mocz, P., Vogelsberger, M., Robles, V. H., et al. 2017, MNRAS, 471, 4559, doi: 10.1093/mnras/stx1887 Moliné, Á., Sánchez-Conde, M. A., Palomares-Ruiz, S., &

    doi:10.1093/mnras/stx1887 2017

  52. [52]

    2017, MNRAS, 466, 4974, doi: 10.1093/mnras/stx026 Muñoz, R

    Prada, F. 2017, MNRAS, 466, 4974, doi: 10.1093/mnras/stx026 Muñoz, R. R., Côté, P., Santana, F. A., et al. 2018, The Astrophysical Journal, 860, 66, doi: 10.3847/1538-4357/aac16b

    doi:10.1093/mnras/stx026 2017

  53. [53]

    O., Drlica-Wagner, A., Bechtol, K., et al

    Nadler, E. O., Drlica-Wagner, A., Bechtol, K., et al. 2021, PhRvL, 126, 091101, doi: 10.1103/PhysRevLett.126.091101

    doi:10.1103/physrevlett.126.091101 2021

  54. [54]

    F., Frenk, C

    Navarro, J. F., Frenk, C. S., & White, S. D. M. 1997, The Astrophysical Journal, 490, 493, doi: 10.1086/304888

    doi:10.1086/304888 1997

  55. [55]

    2021, MNRAS, 501, 1539, doi: 10.1093/mnras/staa3772

    Nori, M., & Baldi, M. 2021, MNRAS, 501, 1539, doi: 10.1093/mnras/staa3772

    doi:10.1093/mnras/staa3772 2021

  56. [56]

    2022, ApJ, 939, 3, doi: 10.3847/1538-4357/ac9303 Pietrzyński, G., Górski, M., Gieren, W., et al

    Pianta, C., Capuzzo-Dolcetta, R., & Carraro, G. 2022, ApJ, 939, 3, doi: 10.3847/1538-4357/ac9303 Pietrzyński, G., Górski, M., Gieren, W., et al. 2009, AJ, 138, 459, doi: 10.1088/0004-6256/138/2/459 Pietrzyński, G., Gieren, W., Szewczyk, O., et al. 2008, The Astronomical Journal, 135, 1993, doi: 10.1088/0004-6256/135/6/1993

    doi:10.3847/1538-4357/ac9303 2022

  57. [57]

    Plummer, H. C. 1911, MNRAS, 71, 460, doi: 10.1093/mnras/71.5.460

    doi:10.1093/mnras/71.5.460 1911

  58. [59]

    I., Mamon, G

    Read, J. I., Mamon, G. A., Vasiliev, E., et al. 2021, MNRAS, 501, 978, doi: 10.1093/mnras/staa3663

    doi:10.1093/mnras/staa3663 2021

  59. [60]

    H., & Matos, T

    Robles, V. H., & Matos, T. 2012, MNRAS, 422, 282, doi: 10.1111/j.1365-2966.2012.20603.x

    arXiv 2012

  60. [61]

    H., Zagorac, J

    Robles, V. H., Zagorac, J. L., & Padmanabhan, N. 2024, MNRAS, 532, 1980, doi: 10.1093/mnras/stae1544

    work page doi:10.1093/mnras/stae1544 2024

  61. [62]

    K., & Peiris, H

    Rogers, K. K., & Peiris, H. V. 2021, Physical Review Letters, 126, 071302, doi: 10.1103/PhysRevLett.126.071302

    doi:10.1103/physrevlett.126.071302 2021

  62. [63]

    Safarzadeh, M., & Spergel, D. N. 2020, ApJ, 893, 21, doi: 10.3847/1538-4357/ab7db2

    work page doi:10.3847/1538-4357/ab7db2 2020

  63. [64]

    L., & Evans, N

    Sanders, J. L., & Evans, N. W. 2020, MNRAS, 499, 5806, doi: 10.1093/mnras/staa2860

    doi:10.1093/mnras/staa2860 2020

  64. [65]

    2014a, Nature Physics, 10, 496, doi: 10.1038/nphys2996

    Schive, H.-Y., Chiueh, T., & Broadhurst, T. 2014a, Nature Physics, 10, 496, doi: 10.1038/nphys2996

    doi:10.1038/nphys2996

  65. [66]

    2020, PhRvL, 124, 201301, doi: 10.1103/PhysRevLett.124.201301

    Schive, H.-Y., Chiueh, T., & Broadhurst, T. 2020, PhRvL, 124, 201301, doi: 10.1103/PhysRevLett.124.201301

    doi:10.1103/physrevlett.124.201301 2020

  66. [67]

    2014b, PhRvL, 113, 261302, doi: 10.1103/PhysRevLett.113.261302

    Schive, H.-Y., Liao, M.-H., Woo, T.-P., et al. 2014b, PhRvL, 113, 261302, doi: 10.1103/PhysRevLett.113.261302

    doi:10.1103/physrevlett.113.261302

  67. [68]

    C., & Engels, J

    Schwabe, B., Niemeyer, J. C., & Engels, J. F. 2016, Physical Review D, 94, 043513, doi: 10.1103/PhysRevD.94.043513

    doi:10.1103/physrevd.94.043513 2016

  68. [69]

    E., Mateo, M., Olszewski, E

    Spencer, M. E., Mateo, M., Olszewski, E. W., et al. 2018, The Astronomical Journal, 156, 257, doi: 10.3847/1538-3881/aae3e4

    doi:10.3847/1538-3881/aae3e4 2018

  69. [70]

    E., Mateo, M., Walker, M

    Spencer, M. E., Mateo, M., Walker, M. G., & Olszewski, E. W. 2017, ApJ, 836, 202, doi: 10.3847/1538-4357/836/2/202

    doi:10.3847/1538-4357/836/2/202 2017

  70. [71]

    J., & Marsh, D

    Stott, M. J., & Marsh, D. J. E. 2018, PhRvD, 98, 083006, doi: 10.1103/PhysRevD.98.083006

    doi:10.1103/physrevd.98.083006 2018

  71. [72]

    S., Chiba, M., et al

    Takada, M., Ellis, R. S., Chiba, M., et al. 2014, Publications of the Astronomical Society of Japan, 66, R1, doi: 10.1093/pasj/pst019

    doi:10.1093/pasj/pst019 2014

  72. [73]

    2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol

    Tamura, N., Takato, N., Shimono, A., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9908, Ground-based and Airborne Instrumentation for Astronomy VI, ed. C. J

    2016

  73. [74]

    Simard, & H

    Evans, L. Simard, & H. Takami, 99081M, doi: 10.1117/12.2232103

    doi:10.1117/12.2232103

  74. [75]

    Toguz, F., Kawata, D., Seabroke, G., & Read, J. I. 2022, MNRAS, 511, 1757, doi: 10.1093/mnras/stac057

    doi:10.1093/mnras/stac057 2022

  75. [76]

    2025, JCAP, 2025, 080, doi: 10.1088/1475-7516/2025/11/080 Van Der Walt, S., Colbert, S

    Totani, T. 2025, JCAP, 2025, 080, doi: 10.1088/1475-7516/2025/11/080 Van Der Walt, S., Colbert, S. C., & Varoquaux, G. 2011, Computing in Science and Engineering, 13, 22, doi: 10.1109/MCSE.2011.37

    doi:10.1088/1475-7516/2025/11/080 2025

  76. [77]

    C., & Schwabe, B

    Veltmaat, J., Niemeyer, J. C., & Schwabe, B. 2018, PhRvD, 98, 043509, doi: 10.1103/PhysRevD.98.043509

    doi:10.1103/physrevd.98.043509 2018

  77. [78]

    E., et al

    Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Medicine, 17, 261, doi: 10.1038/s41592-019-0686-2 17

    doi:10.1038/s41592-019-0686-2 2020

  78. [79]

    G., Mateo, M., & Olszewski, E

    Walker, M. G., Mateo, M., & Olszewski, E. W. 2009a, The Astronomical Journal, 137, 3100, doi: 10.1088/0004-6256/137/2/3100

    doi:10.1088/0004-6256/137/2/3100

  79. [80]

    2009b, The Astronomical Journal, 137, 3109, doi: 10.1088/0004-6256/137/2/3109

    Woodroofe, M. 2009b, The Astronomical Journal, 137, 3109, doi: 10.1088/0004-6256/137/2/3109

    work page doi:10.1088/0004-6256/137/2/3109

  80. [81]

    G., Olszewski, E

    Walker, M. G., Olszewski, E. W., & Mateo, M. 2015, VizieR Online Data Catalog, J/MNRAS/448/2717

    2015

Showing first 80 references.