Pith. sign in

REVIEW 2 major objections 6 minor 52 references

Wide stellar binaries in the ultra-faint dwarf Boötes I can exclude a full dark-matter population of extended, finite-size objects and set a competitive bound on the primordial curvature power spectrum.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-01 15:46 UTC pith:2RONDWSR

load-bearing objection A careful, honest generalization of the Boötes I wide-binary constraint to extended dark objects; the main caveat is the unquantified sensitivity to the assumed initial binary fraction and system age. the 2 major comments →

arxiv 2607.18185 v1 pith:2RONDWSR submitted 2026-07-20 hep-ph astro-ph.CO

Wide binaries in ultra-faint dwarf galaxies as a probe of extended dark objects

Mar\'ia Olalla Olea-Romacho This is my paper
classification hep-ph astro-ph.CO
keywords wide binariesultra-faint dwarf galaxiesextended dark matter objectsimpulsive heatingprimordial power spectrumultracompact minihalosBoötes Idark matter substructure
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.

This paper claims that the wide stellar binaries found in the ultra-faint dwarf galaxy Boötes I act as a gravitational probe that can rule out a full dark-matter population of extended, finite-size objects — not just point-like ones. The author generalizes the standard impulsive-heating calculation for point masses to spherically symmetric perturbers with arbitrary density profiles, parametrized by mass M and radius R90 enclosing 90% of the mass. For objects up to R90 ~ 10^5 solar radii the limits are indistinguishable from point-mass limits, and even for R90 = 10^7 solar radii a 100% dark-matter fraction is excluded; at high mass the limits deepen to fDM ~ 10^-3. Interpreting the r^-3/2 profiles as ultracompact minihalos collapsing at zc = 1200 yields an illustrative upper limit on the primordial curvature power spectrum PR <~ 5x10^-6 over k ~ 4x10^2-3x10^3 Mpc^-1, competitive with the strongest existing small-scale bounds. A sympathetic reader would care because it offers a purely gravitational, model-independent way to constrain extended dark objects such as minihalos, boson stars, and axion miniclusters, and to probe small-scale primordial physics.

Core claim

The central claim is that a population of extended spherical dark objects with a given mass M and radius R90 can be excluded as the dominant dark-matter component by the observed survival of wide binaries in Boötes I. The key insight is that the disruptive heating of a binary by an extended perturber is governed by the projected-mass impulse: the kick on a star is 2GM_2D(b)/(bV), where M_2D(b) is the mass enclosed in a cylinder of radius b around the encounter trajectory. Finite size suppresses disruption when R90 exceeds the strong-deflection radius b90, and more strongly when R90 is comparable to the binary separation; compact objects behave exactly like point masses. The resulting 95% exc

What carries the argument

The central object is the projected-mass impulse: the transverse kick on a star from an extended spherically symmetric perturber is 2GM_2D(b)/(bV), where M_2D(b) is the mass enclosed in a cylinder of radius b around the encounter trajectory. This replaces the point-mass kick and leads to a heating integral whose suppression relative to the point-mass case is R(a) = J_ext(a)/J_point(a). The paper also defines a strong-deflection cutoff b_cut = G[m_b/2 + M_2D(b_cut)]/sigma^2, which reduces to the point-mass b90 for compact objects and regularizes the integral for extended ones. These ingredients convert a catalogue of surviving wide binaries into 95% exclusion curves in the (M, R90) plane.

Load-bearing premise

The whole exclusion rests on the assumption that the binaries observed today in Boötes I formed early and have been evolving for the full 13 Gyr age of the old stellar population, with an initial binary fraction of 2.5% and a separation distribution dN/ds ~ s^-1.6; if binaries formed later or at a different intrinsic rate, the room for dark-perturber disruption shrinks and all quoted limits shift upward.

What would settle it

Measure the separation distribution of wide binaries in Boötes I at separations between 16000 and ~50000 au; under the model with fDM at the quoted limits, the survival probability drops steeply, so a robust detection of several pairs at those separations would directly conflict with the exclusion.

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

If this is right

  • If these limits hold, dark matter cannot be fully composed of extended objects in the mass range ~0.1-3000 M_sun for radii up to 10^7 R_sun; at high masses the allowed dark-matter fraction drops to ~10^-3.
  • Compact objects with R90 below the strong-deflection radius b90 are dynamically indistinguishable from black holes of the same mass, so the point-mass bounds are robust for such sizes.
  • The constraints extend to sizes unreachable by microlensing and complement the Icarus caustic-crossing limits, jointly excluding fDM = 1 over many decades in mass.
  • For ultracompact minihalos, the implied bound on the primordial curvature power spectrum (PR ~ few x 10^-6 over k ~ 4x10^2-3x10^3 Mpc^-1) is competitive with CMB y/mu distortions and Icarus where they overlap.
  • The constraints are conservative because they omit the single-encounter catastrophic disruption channel, so including it would only strengthen the exclusions.

Where Pith is reading between the lines

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

  • The author leaves implicit that the size-dependent suppression could be used to measure the density profile of a detected extended dark object population, rather than just bound its abundance; future data might distinguish NFW from r^-3/2 by the shape of the exclusion curve.
  • The UCMH recast assumes a monochromatic mass-scale mapping and neglects the cloud-in-cloud problem; extending it to an extended mass function would turn the single-number bound into a family of constraints on the shape of the primordial spectrum.
  • A natural test of the framework is to search for ultra-wide binaries at separations just beyond the current counting window in Boötes I; the model predicts a steep survival cutoff that could be observed with deeper imaging.
  • If wide-binary surveys in several ultra-faint dwarfs become available, the combined likelihood could sharpen the limits and potentially probe the radial distribution of extended objects within dwarf galaxies.

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

2 major / 6 minor

Summary. This manuscript generalizes the impulsive-disruption treatment of wide binaries by point-mass dark objects to spherical extended dark objects (EDOs). For an extended perturber, the transverse kick on a star is expressed in terms of the mass M2D(b) enclosed in an infinite cylinder of radius b around the trajectory, leading to an orientation-averaged heating integral J(a) and a diffusive disruption time text_dis. A self-consistent strong-deflection cutoff bcut = G(mb/2 + M2D(bcut))/σ^2 reduces to the point-mass b90 in the compact limit. The author uses this framework to derive 95% exclusion limits on the dark-matter fraction fDM as a function of mass M and radius R90 for NFW, r^-3/2, and r^-9/4 density profiles, with R90 from 10^4 to 10^7 R_sun. Compact objects converge to point-like behavior, while large objects weaken the limits by one to two orders of magnitude. The r^-3/2 results are mapped onto ultracompact minihalos collapsing at zc=1200, yielding an illustrative constraint on the primordial curvature power spectrum, PR ≲ 5e-6 over k ≈ 4e2-3e3 Mpc^-1. The analysis follows Shariat et al. for the Boötes I inputs and treats stellar flybys and catastrophic collisions conservatively.

Significance. If taken at face value, the paper provides a useful model-agnostic extension of the newly available ultra-faint-dwarf wide-binary probe from point masses to the (M, R90) plane of extended dark objects, complementing microlensing and caustic-crossing constraints. The derivation is transparent and has real strengths: the point-mass limit is recovered by construction; the projected-mass impulse is a clean analytic generalization; the three benchmark profiles bracket plausible substructure models; and the UCMH-to-PR recast is clearly labeled as illustrative. I checked the quoted compact limit and the UCMH arithmetic; the internal consistency is good. The principal weakness is that the exclusion curves and the PR bound are conditional on an assumed initial wide-binary population, and this dependence is acknowledged but not quantified. A sensitivity scan would materially strengthen the paper.

major comments (2)
  1. [Sec. IIA-IIB, Eq. (3)] The exclusion curves in Figs. 2-3 and the PR curve in Fig. 4 are computed from Eq. (3) with N_wb,0 = 287.5 (f_wb,0 = 2.5% of N_tot ≈ 11500), p(s) ∝ s^-1.6 over [5000 au, ∞), and t_age = 13 Gyr. Section IIA states that the formation history is 'not fully understood' and that the constraints depend on the effective time over which perturbations have acted, but the paper does not quantify this dependence. Because text_dis is inversely proportional to fDM, a factor-of-two change in t_age shifts the required f_lim by roughly a factor of two; a different f_wb,0 shifts N0 and hence the threshold fDM in a logarithmic but non-negligible way. The erfc inversion in Eq. (22) amplifies these shifts into PR. I request a sensitivity scan over e.g. t_age = 5-13 Gyr and f_wb,0 = 1-5% for representative (M, R90), and a qualified wording such as 'under the benchmark initial-population assumptions' for the
  2. [Sec. V, Eqs. (19)-(22)] The recast from f_lim to PR relies on the monochromatic M(k) mapping, the choice zc = 1200, the fitted δmin form of Eq. (23), and the assumptions of no cloud-in-cloud, no mass growth, and no tidal survival. The text lists these limitations, and the result is called 'illustrative', but Fig. 4 shows a single red curve and the conclusion describes it as 'competitive with the strongest existing small-scale bounds'. Since β enters through erfc^{-1}(2β), the curve is exponentially sensitive to the input assumptions; even a modest change in the effective surviving fraction of UCMHs or in the collapse threshold can shift PR by a large factor. Please show at least one bracketing variant (for example a lower zc or a reduced surviving minihalo fraction) so the reader can assess the robustness of the overlap claim, or consistently downgrade the wording to 'illustrative upper envelope' throughout.
minor comments (6)
  1. [Sec. V, Eq. (23)] There is a missing reference after 'with the scale factor' — an empty citation placeholder.
  2. [Sec. III, Eq. (15)] Eq. (15) is an implicit equation for bcut. For the truncated profiles used here a solution exists, but the text does not state how it is solved or confirm uniqueness. Please add a sentence on the solution procedure and, ideally, a test of sensitivity to the cutoff convention.
  3. [Figs. 1-4] The axis label 'M [M ¯]' is garbled; it should be M [M_sun] (or the equivalent). The same overline symbol appears in several figure labels.
  4. [Abstract and Sec. IIA] The spelling of 'Boötes I' is inconsistent: the abstract uses 'Bootes I' while the body uses 'Boötes I'. Please unify.
  5. [Sec. IIB, after Eq. (2)] The statement that the catastrophic channel never turns on because a_fringe ≫ 16000 au is asserted without a numerical value. Giving a_fringe for the benchmark inputs would make the criterion transparent.
  6. [Sec. IV, NFW convention] The NFW truncation concentration c = 100 is a shape convention. A brief remark on how R90/rt changes with c, and whether the main conclusions are sensitive to this choice, would be useful.

Circularity Check

0 steps flagged

No significant circularity: the extended-perturber exclusion is anchored to external point-mass and binary-population inputs, with the main assumptions explicitly flagged in the paper.

full rationale

The derivation chain is not circular. The initial wide-binary population (f_wb,0=2.5%, dN/ds∝s^-1.6, t_age=13 Gyr) and environmental inputs (ρ_DM, σ*, σ_p) are taken from the cited Boötes I analysis [2] and external catalogues, not fitted here; Sec. IIA explicitly says 'Their formation history is not fully understood' and that the constraints depend on the effective time, which is a stated modeling sensitivity rather than a definitional reduction. The extended-perturber rate is built from the projected-mass impulse (Eqs. 4-14); the 1/8 prefactor is fixed so the compact limit reproduces the published point-mass disruption time (Eq. 2), which is a consistency anchor, not a fit to the quantity being predicted. The new content—suppression R(a)=J_ext/J_point and the f_lim(M,R90) plane—follows from the profile-convolved M_2D(b) and is not an input. The UCMH recast (Eqs. 18-22) uses standard mass-radius and erfc-inversion relations with δ_min from Ref. [48]; its limitations (cloud-in-cloud, fixed profile, no late-time survival) are listed in Sec. V and are modeling caveats. The author's self-citations [8,9] occur only in the prompt-cusps review list and are not load-bearing. No step reduces the claimed output to its input by construction.

Axiom & Free-Parameter Ledger

11 free parameters · 10 axioms · 0 invented entities

The paper contributes no new free parameters fitted to its own data: every number entering the constraints is either inherited from cited measurements (binary fraction, densities, dispersions, catalogue) or chosen as a stated convention (NFW concentration, z_c, two-point δ_min fit). The genuinely new theoretical content is the finite-size suppression factor R(a), computed from known impulse physics. No new physical entities are introduced; 'extended dark objects' is a two-parameter (M, R90) parametrization of existing candidates (UCMHs, prompt cusps, boson stars, axion miniclusters).

free parameters (11)
  • f_wb,0 (initial wide-binary fraction) = 2.5% → N_wb,0 = 287.5
    Inherited from Shariat et al. [2]; N_pred scales directly with it via Eq. (3).
  • separation distribution exponent = -1.6 (dN/ds ∝ s^-1.6)
    From [30,42]; sets N0(9-16 kau) = 59.0 in Eq. (1).
  • t_age (system age) = 13 Gyr
    Assumed binary-evolution time; paper flags that formation history is unknown, so constraints depend on the effective perturbation time.
  • ρ_DM (Boötes I) = 0.158 M⊙/pc^3
    From Hayashi et al. [43]; sets perturber number density n = fDM ρ_DM / M.
  • σ_rel (effective encounter speed) = 9.66 km/s (σ_p = 8.50 km/s)
    From Graham & Ramani [24]; sets V in the impulse and all encounter rates.
  • m_b (typical binary mass) = 0.6 M⊙
    From [2]; enters b_cut, b90, and the energy scale.
  • NFW truncation concentration c = 100 (R90/rt = 0.69)
    Shape convention required because NFW has two scale lengths; from Ref. [49].
  • z_c (UCMH collapse redshift) = 1200
    Adopted formation epoch; sets the R90(M) track of Eq. (18).
  • δ_min_χ(k0), c_δ = 1.03×10^-2 at k0 = 3 Mpc^-1; c_δ = 2.911
    Two-point fit to values quoted from Ref. [48]; stated to affect the P_R normalization by ~10%.
  • 1/8 prefactor in J(a) = 1/8
    Calibration constant fixed so the compact limit reproduces the published point-mass disruption time (Eq. 2); cancels in the suppression ratio R(a).
  • k_cat (catastrophic timescale constant) = 0.07
    From [20]; inactive in the regime considered since a_fringe ≫ 16000 au.
axioms (10)
  • domain assumption Impulse approximation: straight-line encounters at a single effective speed V = σ_rel
    Sec. III opening: justified by σ_rel = 9.66 km/s ≫ binary orbital speed ~0.3 km/s at 10^4 au, the same argument as the point-mass analysis.
  • standard math Projected-mass kick: Δv⊥ = 2GM2D(b)/(bV); mass outside the impact cylinder exerts no net transverse impulse (Eq. 4)
    Newtonian impulse; M2D construction follows Wright & Brainerd [47] via Eqs. (5)-(6).
  • standard math The linear-in-kick heating term averages to zero over isotropic orientations and phases; mean heating ∝ ⟨|Δv_rel|^2⟩
    Standard treatment from the point-mass impulsive-heating literature (Binney & Tremaine [20]).
  • ad hoc to paper b_cut prescribed by Eq. (15): b_cut = G[m_b/2 + M2D(b_cut)]/σ^2
    'we adopt the following estimate' — introduced here to regularize the small-b divergence; reduces exactly to b90 for point masses.
  • domain assumption Catastrophic single-flyby channel is inactive (a_fringe ≫ 16000 au) and is omitted
    Sec. IIB; omission only underestimates disruption, making limits conservative.
  • domain assumption Stellar flybys are excluded from P_surv
    Sec. IIB; conservative because it over-predicts survivors.
  • standard math Poisson statistics: 95% exclusion when N_pred = µ_crit = 14.07 for N_obs = 21
    Sec. IIB; N_obs = ⌊43/2⌋ from the published catalogue.
  • domain assumption UCMH mapping: Gaussian scale-invariant P_R; one mode ↔ one halo mass (Eq. 20); collapse by z_c = 1200; σ_χ,H^2 = 0.91 P_R; f_DM = β; no cloud-in-cloud removal; all UCMHs survive to z = 0
    Sec. V; the paper explicitly flags each as a limitation; the no-survival assumption makes the bound optimistic.
  • ad hoc to paper δ_min_χ(k) logarithmic form (Eq. 23) with constants fitted to two Ref. [48] values
    One-parameter interpolating form; residual freedom stated to affect the bound by ~10%.
  • domain assumption Truncated power-law profiles with M(<R90) = 0.9M fixing r_t (Eq. 17); NFW c = 100 convention
    Profile conventions bracket the concentrations of dark-matter substructure; the P_R recast uses the r^-3/2 track only.

pith-pipeline@v1.3.0-alltime-deepseek · 13005 in / 31282 out tokens · 267892 ms · 2026-08-01T15:46:02.318833+00:00 · methodology

0 comments
read the original abstract

Wide stellar binaries are sensitive dynamical probes of dark matter substructure. We generalize existing point-mass disruption constraints to spherical extended dark objects and apply the resulting framework to the population of wide-binary candidates identified in the ultra-faint dwarf galaxy Bootes I. We derive 95% confidence limits on the dark matter fraction as a function of the perturber mass, the radius enclosing 90% of the mass, and the density profile, considering Navarro-Frenk-White, r^-3/2, and r^-9/4 models. Sufficiently compact objects converge to the point-mass limit, whereas finite size suppresses binary disruption when the perturber becomes comparable to the relevant encounter and binary scales. The constraints remain sensitive to dark matter fractions well below unity over a broad region of the mass-radius plane and extend to objects substantially larger than those accessible to conventional microlensing searches. As an application, we map the r^-3/2 results onto ultracompact minihalos and derive an illustrative constraint on the primordial curvature power spectrum. Ultra-faint-dwarf wide binaries therefore offer a purely gravitational probe of the abundance of extended dark matter objects and of the small-scale primordial curvature power spectrum.

Figures

Figures reproduced from arXiv: 2607.18185 by Mar\'ia Olalla Olea-Romacho.

Figure 1
Figure 1. Figure 1: FIG. 1: Suppression of the diffusive wide-binary heating rate, [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Illustrative [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

52 extracted references · 36 linked inside Pith

  1. [1]

    B. Carr, A. J. Iovino, G. Perna, V. Vaskonen, and H. Veermäe, Riv. Nuovo Cim.49, 225 (2026), arXiv:2601.06024 [astro-ph.CO]

    arXiv 2026

  2. [2]

    Shariatet al., Publ

    C. Shariatet al., Publ. Astron. Soc. Pac.137, 104103 (2025), arXiv:2509.04555 [astro-ph.GA]

    arXiv 2025

  3. [3]

    M. S. Delos, A. L. Erickcek, A. P. Bailey, and M. A. Al- varez, Phys. Rev. D98, 063527 (2018), arXiv:1806.07389 [astro-ph.CO]

    Pith/arXiv arXiv 2018

  4. [4]

    Bringmann, P

    T. Bringmann, P. Scott, and Y. Akrami, Phys. Rev. D 85, 125027 (2012)

    2012

  5. [5]

    Ricotti and A

    M. Ricotti and A. Gould, Astrophys. J.707, 979 (2009), arXiv:0908.0735 [astro-ph.CO]

    Pith/arXiv arXiv 2009

  6. [6]

    M. S. Delos and S. D. M. White, JCAP10, 008 (2023), 2209.11237

    Pith/arXiv arXiv 2023

  7. [7]

    M. S. Delos, M. Bruff, and A. L. Erickcek, Phys. Rev. D 100, 023523 (2019), arXiv:1905.05766 [astro-ph.CO]. 9

    Pith/arXiv arXiv 2019

  8. [8]

    M. O. Olea-Romacho, M. Fairbairn, and P. Ralegankar, SciPost Phys.20, 044 (2026), arXiv:2507.18692 [hep-ph]

    arXiv 2026

  9. [9]

    M. O. Olea-Romacho, Phys. Rev. D113, 063503 (2026), arXiv:2511.05240 [hep-ph]

    arXiv 2026

  10. [10]

    D. J. Kaup, Phys. Rev.172, 1331 (1968)

    1968

  11. [11]

    Visinelli, Int

    L. Visinelli, Int. J. Mod. Phys. D30, 2130006 (2021), arXiv:2109.05481 [gr-qc]

    Pith/arXiv arXiv 2021

  12. [12]

    M.Fairbairn, D.J.E.Marsh, J.Quevillon, andS.Rozier, Phys. Rev. D97, 083502 (2018), arXiv:1707.03310 [astro- ph.CO]

    Pith/arXiv arXiv 2018

  13. [13]

    C. J. Hogan and M. J. Rees, Phys. Lett. B205, 228 (1988)

    1988

  14. [14]

    E. W. Kolb and I. I. Tkachev, Phys. Rev. Lett.71, 3051 (1993), arXiv:hep-ph/9303313

    Pith/arXiv arXiv 1993

  15. [15]

    Croon, D

    D. Croon, D. McKeen, and N. Raj, Phys. Rev. D101, 083013 (2020), arXiv:2002.08962 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  16. [16]

    Croon, D

    D. Croon, D. McKeen, N. Raj, and Z. Wang, Phys. Rev. D102, 083021 (2020), arXiv:2007.12697 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  17. [17]

    P. L. Kellyet al., Science347, 1123 (2015), arXiv:1411.6009 [astro-ph.CO]

    Pith/arXiv arXiv 2015

  18. [18]

    P. L. Kellyet al., Nature Astron.2, 334 (2018), arXiv:1706.10279 [astro-ph.GA]

    Pith/arXiv arXiv 2018

  19. [19]

    Croon, B

    D. Croon, B. Crossey, J. M. Diego, B. J. Kavanagh, and J. M. Palencia, Phys. Rev. D113, 063017 (2026), arXiv:2511.20761 [astro-ph.CO]

    arXiv 2026

  20. [20]

    Binney and S

    J. Binney and S. Tremaine,Galactic Dynamics: Second Edition(2008)

    2008

  21. [21]

    Peñarrubia, Monthly Notices of the Royal Astronomical Society484, 5409 (2019), https://academic.oup.com/mnras/article- pdf/484/4/5409/27790551/stz338.pdf

    J. Peñarrubia, Monthly Notices of the Royal Astronomical Society484, 5409 (2019), https://academic.oup.com/mnras/article- pdf/484/4/5409/27790551/stz338.pdf

    2019

  22. [22]

    Hamilton and S

    C. Hamilton and S. Modak, Monthly Notices of the Royal Astronomical Society532, 2425 (2024), https://academic.oup.com/mnras/article- pdf/532/2/2425/58535876/stae1654.pdf

    2024

  23. [23]

    T. D. Brandt, Astrophys. J. Lett.824, L31 (2016), arXiv:1605.03665 [astro-ph.GA]

    Pith/arXiv arXiv 2016

  24. [24]

    P. W. Graham and H. Ramani, Phys. Rev. D110, 075012 (2024), arXiv:2404.01378 [hep-ph]

    Pith/arXiv arXiv 2024

  25. [25]

    S. Ando, N. Hiroshima, and K. Ishiwata, Phys. Rev. D 106, 103014 (2022), arXiv:2207.05747 [astro-ph.CO]

    Pith/arXiv arXiv 2022

  26. [26]

    Paré and J

    T. Paré and J. Lavalle, (2026), arXiv:2606.14827 [astro- ph.CO]

    Pith/arXiv arXiv 2026

  27. [27]

    J. N. Bahcall, P. Hut, and S. Tremaine, Astrophys. J. 290, 15 (1985)

    1985

  28. [28]

    M. D. Weinberg, S. L. Shapiro, and I. Wasserman, As- trophys. J.312, 367 (1987)

    1987

  29. [29]

    E. D. Ramirez and M. R. Buckley, Mon. Not. Roy. As- tron. Soc.525, 5813 (2023), arXiv:2209.08100 [hep-ph]

    Pith/arXiv arXiv 2023

  30. [30]

    J. Yoo, J. Chaname, and A. Gould, Astrophys. J.601, 311 (2004), arXiv:astro-ph/0307437

    Pith/arXiv arXiv 2004

  31. [31]

    D. P. Quinn, M. I. Wilkinson, M. J. Irwin, J. Marshall, A. Koch, and V. Belokurov, Mon. Not. Roy. Astron. Soc. 396, 11 (2009), arXiv:0903.1644 [astro-ph.GA]

    Pith/arXiv arXiv 2009

  32. [32]

    M. A. Monroy-Rodríguez and C. Allen, Astrophys. J. 790, 159 (2014), arXiv:1406.5169 [astro-ph.GA]

    Pith/arXiv arXiv 2014

  33. [33]

    Tyler, A

    E. Tyler, A. M. Green, and S. P. Goodwin, Mon. Not. Roy. Astron. Soc.524, 3052 (2023), arXiv:2207.08668 [astro-ph.GA]

    Pith/arXiv arXiv 2023

  34. [34]

    J. I. Read, J. Phys. G41, 063101 (2014), arXiv:1404.1938 [astro-ph.GA]

    Pith/arXiv arXiv 2014

  35. [35]

    Jiang and S

    Y.-F. Jiang and S. Tremaine, Mon. Not. Roy. Astron. Soc.401, 977 (2010), arXiv:0907.2952 [astro-ph.GA]

    Pith/arXiv arXiv 2010

  36. [36]

    Ivezićet al.(LSST), Astrophys

    Ž. Ivezićet al.(LSST), Astrophys. J.873, 111 (2019), arXiv:0805.2366 [astro-ph]

    Pith/arXiv arXiv 2019

  37. [37]

    Tsiane, S

    K. Tsiane, S. Mau, A. Drlica-Wagner, J. L. Carlin, P. S. Ferguson, K. Bechtol, E. O. Nadler, A. H. G. Peter, Y.-Y. Mao, and A. J. Thornton (LSST DESC), Open J. Astro- phys.8, 142072 (2025), arXiv:2504.16203 [astro-ph.GA]

    Pith/arXiv arXiv 2025

  38. [38]

    Drlica-Wagneret al.(LSST Dark Matter Group), (2019), arXiv:1902.01055 [astro-ph.CO]

    A. Drlica-Wagneret al.(LSST Dark Matter Group), (2019), arXiv:1902.01055 [astro-ph.CO]

    Pith/arXiv arXiv 2019

  39. [39]

    E. O. Nadler, V. Gluscevic, T. Driskell, R. H. Wechsler, L. A. Moustakas, A. Benson, and Y.-Y. Mao, Astrophys. J.967, 61 (2024), arXiv:2401.10318 [astro-ph.GA]

    Pith/arXiv arXiv 2024

  40. [40]

    J. F. Navarro, C. S. Frenk, and S. D. M. White, Astro- phys. J.462, 563 (1996), arXiv:astro-ph/9508025

    Pith/arXiv arXiv 1996

  41. [41]

    Caputo, G

    A. Caputo, G. M. Tomaselli, and C. Hamilton, (2026), arXiv:2607.12011 [astro-ph.GA]

    Pith/arXiv arXiv 2026

  42. [42]

    El-Badry and H.-W

    K. El-Badry and H.-W. Rix, Monthly Notices of the Royal Astronomical Society: Letters482, L139 (2019)

    2019

  43. [43]

    Hayashi, Y

    K. Hayashi, Y. Hirai, M. Chiba, and T. Ishiyama, As- trophys. J.953, 185 (2023), arXiv:2206.02821 [astro- ph.GA]

    Pith/arXiv arXiv 2023

  44. [44]

    S. A. Jenkins, T. S. Li, A. B. Pace, A. P. Ji, S. E. Koposov, and B. Mutlu-Pakdil, Astrophys. J.920, 92 (2021), arXiv:2101.00013 [astro-ph.GA]

    Pith/arXiv arXiv 2021

  45. [45]

    Peñarrubia, A

    J. Peñarrubia, A. D. Ludlow, J. Chanamé, and M. G. Walker, Mon. Not. Roy. Astron. Soc.461, L72 (2016), arXiv:1605.09384 [astro-ph.GA]

    Pith/arXiv arXiv 2016

  46. [46]

    Longhitano and B

    M. Longhitano and B. Binggeli, Astron. Astrophys.509, A46 (2010), arXiv:1001.3819 [astro-ph.SR]

    Pith/arXiv arXiv 2010

  47. [47]

    C. O. Wright and T. G. Brainerd, Astrophys. J.534, 34 (2000)

    2000

  48. [48]

    Bringmann, D

    T. Bringmann, D. Croon, and S. Sevillano Muñoz, (2025), arXiv:2506.20704 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  49. [49]

    Croon and S

    D. Croon and S. Sevillano Muñoz, Eur. Phys. J. C85, 8 (2025), arXiv:2407.02573 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  50. [50]

    J. R. Bond, S. Cole, G. Efstathiou, and N. Kaiser, As- trophys. J.379, 440 (1991)

    1991

  51. [51]

    Ricotti, J

    M. Ricotti, J. P. Ostriker, and K. J. Mack, Astrophys. J.680, 829 (2008), 0709.0524

    Pith/arXiv arXiv 2008

  52. [52]

    Chluba, A

    J. Chluba, A. L. Erickcek, and I. Ben-Dayan, Astrophys. J.758, 76 (2012), arXiv:1203.2681 [astro-ph.CO]

    Pith/arXiv arXiv 2012