Pith. sign in

REVIEW 3 major objections 6 minor 1 cited by

Probing the fate of large primordial perturbations with exoplanets

T0 review · 3 major / 6 minor · reviewed 2026-07-12 · grok-4.5

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

Pith's one-line read Ultra-wide exoplanets already set competitive limits on large primordial density peaks that would seed ultra-compact dark minihalos.

desk verdict Solid new dynamical probe that converts non-disruption of a dozen ultra-wide exoplanets into competitive PPS peak limits via a careful UCMH population model; the statistics are the softest link but not fatal. read the letter →

arxiv 2606.14827 v2 pith:63GJYX4N submitted 2026-06-12 astro-ph.CO astro-ph.EPastro-ph.GAhep-ph

Théo Paré , Julien Lavalle This is my paper · ORCID
classification astro-ph.COastro-ph.EPastro-ph.GAhep-ph PACS 12.60.-i95.35.+d98.35.Gi
keywords ultra-wideexoplanetsultra-compactminihalosprimordialpowerspectrumimpulsiveheatingdarkmattersubstructuredynamicalconstraints
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that planets on extremely wide orbits around their stars act as sensitive gravitational thermometers for compact dark objects that may populate the Galaxy. If the primordial density spectrum rose sharply on small scales, those peaks would collapse into dense ultra-compact minihalos. Repeated fly-bys of such minihalos would inject enough energy to unbind the loosest planetary systems. Because a dozen known wide-orbit planets are still bound after several billion years, the amplitude of any such primordial peak is already limited at levels competitive with cosmic-microwave-background and pulsar-timing bounds. Future direct-imaging surveys that find more of these fragile systems will tighten the limits further, and the same heating can leave a distinctive orbital-misalignment signature that would positively identify a dark-object population.

What carries the argument

Impulsive heating rate of a planet–star binary by a Galactic population of ultra-compact minihalos, converted into a Poisson survival probability and combined across systems into a global P_surv that is compared with nσ thresholds.

What would settle it

Discovery of even one additional, older, more loosely bound planet whose calculated heating-to-binding ratio exceeds unity under the same minihalo population would push the global survival probability below the claimed nσ contour and falsify or tighten the exclusion.

Watch

Extended reading notes

Core claim

A carefully selected sample of twelve ultra-wide-orbit exoplanets already excludes primordial power-spectrum peaks of amplitude A• ≳ 10^{-4}–10^{-2} on comoving scales k• ∼ 10^2–10^4 Mpc^{-1} that would produce ultra-compact minihalos heavier than ∼10^5 solar masses, at 1–5σ depending on whether pre-accreted minihalos are counted.

Load-bearing premise

Each planet’s survival probability is treated as statistically independent and is computed from a Poisson number of encounters whose mean is fixed by a semi-analytic model of the local ultra-compact-minihalo density; any residual correlation or density error simply rescales the global exclusion.

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 / 6 minor

Summary. The paper proposes ultra-wide-orbit exoplanets as a dynamical probe of Galactic compact dark-matter objects, specializing to ultra-compact minihalos (UCMHs) formed from a peaked enhancement of the primordial power spectrum. Impulsive heating of a planet–star system is derived in the weak-encounter limit (Eqs. 2–11), disruption is diagnosed via a heating-to-binding ratio R_heat (Eq. 13), and a Poisson encounter model is used to define individual disruption probabilities that are multiplied into a global survival probability P_surv (Eq. 22). A semi-analytic excursion-set/merger-tree UCMH population (App. A), including tidal stripping, is mapped onto the two peak parameters (A•, k•). From a catalogue cut yielding twelve systems (Table I, Fig. 2), the authors report 1–5σ exclusions on large-amplitude peaks that produce UCMHs ≳10^5 M⊙ (Fig. 4), and they derive adiabatic-invariant evolution equations for semi-major axis, eccentricity, and inclination as potential positive signatures (Sect. V, App. B).

Significance. If the statistical combination and local UCMH density are under control, the work opens a genuinely new dynamical channel for small-scale primordial power, complementary to CMB, Lyman-α, spectral distortions, and PTA limits, and it is well timed for Roman and ELT direct-imaging yields. Strengths that should be credited include: (i) a self-contained EST-based UCMH mass function and host-halo merger tree (App. A) that cleanly links A• and k• to a Galactic population; (ii) closed-form orbital-evolution equations from actions (Eqs. 27–28, App. B) that make a falsifiable multi-planet inclination signature; and (iii) an explicit mock-population check against selection bias (App. C). The result is therefore of clear interest to both cosmology and exoplanetary dynamics, provided the load-bearing statistical steps are tightened.

major comments (3)
  1. Eq. (22) and surrounding text in Sect. IV define the nσ contours of Fig. 4 from the product of individual survival probabilities, treating the twelve systems as statistically independent. Fig. 2 shows that all selected systems lie within a few hundred parsecs to ~kpc of the Sun and therefore sample essentially the same local UCMH density and velocity field. Any residual spatial correlation or shared systematic in the App. A merger-tree/tidal-stripping prediction multiplies rather than averages in P_surv. The manuscript should either (a) quantify the impact of a coherent shift in local n• (or of a modest correlation coefficient) on the 3–5σ contours, or (b) report single-system and leave-one-out limits alongside the product so that the headline exclusion is not driven solely by the independence assumption.
  2. In the light-UCMH regime that sets the tightest bounds (b_min ≪ R_p; cf. the asymptotic scalings after Eq. 13 and the estimate in Eq. 19), the mean encounter number N_bar (Eq. 15) is typically ≪1. Disruption then sits in the Poisson tail of Eq. (17)–(18), which is sensitive to the precise local density, to 〈v_rel〉, and to the somewhat conventional b_max cut in Eq. (12). A 30–50% coherent uncertainty in the predicted local UCMH density (or a change in the b_max prescription) would rescale A• at fixed CL by a comparable factor. The paper should propagate these systematics into the exclusion bands of Fig. 4 (or show a dedicated sensitivity plot) rather than presenting only the two discrete ‘conservative/optimistic f’ curves.
  3. The disruption criterion R_heat ≥ 1 (Eq. 13) is converted to a Poisson probability of ‘enough’ encounters, each depositing the average heat 〈δε〉. For rare, high-impact encounters this mean-field step can mis-estimate the true disruption probability relative to a Monte-Carlo sampling of the full (m•, b) distribution. At minimum, the authors should validate the Poisson-plus-mean-heat approximation against a direct Monte-Carlo of encounter histories for a representative subset of the twelve systems (especially those with the largest R_p T / m⋆ in Table I), and state the fractional change in P_disr.
minor comments (6)
  1. Numerous typographical and spacing errors remain (e.g. abstract ‘noval’; p. 2 ‘deonstrate’, ‘indentical’; ‘Obvioulsy’; section headers with broken spaces such as ‘HEA TING’, ‘POPULA TION’; ‘seee.g.’). A full proof-read is needed.
  2. Fig. 4 left panel: the 1–5σ curves for conservative vs optimistic f are hard to distinguish at small k; a clearer linestyle/legend or separate panels would help.
  3. Eq. (12): the numerical prefactor in b_max = 〈v_rel〉 P / (3√3) is not derived in the text; a one-line justification (or a reference to the exact impulse-duration criterion) would improve reproducibility.
  4. Table I lists twelve systems but the text says ‘a selected sample of 128 objects’ and ‘the 10 most constraining… with 8 common’. A short table or appendix listing the full cut criteria and the discarded objects would make the sample transparent.
  5. App. A, Eq. (A17)–(A19): the (G0, γ1, γ2) = (0.57, 0.38, −0.01) correction is taken from the literature; state explicitly whether results change under pure Press–Schechter (no G factor), at least for the UCMH fraction F_host•.
  6. Sect. V / Fig. 5: the analytic low-e solutions underestimate a(t) and overestimate e(t); the text already notes this, but quoting the fractional error on t_ej (~20%) in the caption would help readers who use only the analytic formulae.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: exoplanet catalogue is external data fed into a forward UCMH population model whose free parameters are the PPS peak parameters being constrained.

full rationale

The derivation chain is self-contained and non-circular. The heating rate (Eqs. 8–11), disruption criterion (Eq. 13), Poisson encounter statistics (Eqs. 14–18), and global survival probability (Eq. 22) are standard dynamical constructions applied to an external exoplanet catalogue (exoplanet.eu). The only free parameters of the model are the two PPS peak parameters (A•, k•) that are being constrained; no quantity is fitted to the exoplanet sample and then re-used as a prediction. The Galactic UCMH mass function and tidal-stripping model of App. A are built from excursion-set theory plus the authors’ earlier semi-analytic machinery (Refs. [71, 73, 74, 86]), but those citations supply an independent forward model of structure formation, not a result that already encodes the exoplanet survival data. The orbital-evolution signatures of Sect. V follow from adiabatic invariants and are likewise independent of the exclusion contours. The softest links (independence of the twelve systems, Poisson assumption for N̄ ≪ 1) are modelling assumptions that affect the numerical strength of the limits, not circular reductions of the claimed derivation. Score 1 reflects only the minor, non-load-bearing self-citation of the authors’ prior tidal-stripping papers.

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

The central claim rests on standard stellar-dynamics and structure-formation machinery plus a handful of modelling choices that convert an observed catalogue into PPS limits. No new particles or forces are postulated; the free parameters are the two that are being constrained.

free parameters (4)
  • A• (peak amplitude)
    Free parameter of the injected PPS peak; the quantity being constrained, not fitted a priori.
  • k• (peak injection scale)
    Second free parameter of the PPS peak; likewise constrained rather than fitted.
  • local DM density ρ_dm(⊙)
    Taken from McMillan 2017 NFW fit (∼0.01 M⊙ pc^{-3}); enters the encounter rate linearly.
  • relative velocity 〈v_rel〉
    Set to ∼300 km s^{-1}; appears in both the heating rate and the impact-parameter cut-offs.
assumptions (5)
  • domain assumption Impulsive, weak-encounter approximation (deflection angle ≪ π/2, positions fixed during fly-by)
    Used from Eq. (2) onward; standard for wide binaries but becomes marginal for the closest encounters.
  • domain assumption Number of encounters follows a Poisson distribution with mean fixed by the local UCMH density and b_max
    Eq. (17); converts mean heating into a disruption probability.
  • domain assumption UCMH population fully predicted by excursion-set theory with a δ-function peak in the PPS plus the semi-analytic merger tree of App. A
    Core of Sect. IV and App. A; inherits all standard EST assumptions (sharp-k filter, spherical collapse barrier, etc.).
  • ad hoc to paper Individual planet survival probabilities are statistically independent
    Explicitly stated before Eq. (22); allows the product form of the global survival probability.
  • domain assumption Ages of the selected exoplanets equal the ages of their host stars and are accurately known
    Used to compute total injected energy; justified by stellar-evolution arguments but carries observational uncertainty.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Probing the fate of large primordial perturbations with exoplanets." pith.science (2026). https://pith.science/paper/63GJYX4N

@misc{pith2026260614827,
  author       = {Pith},
  title        = {Pith review of: Probing the fate of large primordial perturbations with exoplanets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/63GJYX4N}},
  note         = {Machine review of arXiv:2606.14827}
}
read the original abstract

We propose ultra-wide-orbit exoplanets as a novel probe of small-scale dark matter objects. These systems are highly sensitive to gravitational perturbations that could be induced by a Galactic population of compact baryon-free dark matter objects -- whether point-like or extended. Focusing on ultra-compact minihalos, which may arise from large primordial perturbations deviating from the canonical scale-invariant power spectrum, we derive new constraints on their injection scale and amplitude. These constraints complement existing dynamical limits and are expected to improve with upcoming exoplanet surveys. Furthermore, the detection of additional loosely bound exoplanets with these surveys could significantly tighten these constraints. Beyond constraints, we also identify characteristic observational signatures in these systems that could help trace a population of dark matter objects. All this strengthens the potential of exoplanetary science to probe the dark universe back to its very primordial properties.

Figures

Figures reproduced from arXiv: 2606.14827 by the authors.

Figure 1
Figure 1. FIG. 1. Hyperbolic encounter between a DMO and a simple [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Distribution of exoplanets by distance to the Sun and [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Prediction of the DM subhalo mass function for a [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Subhalo mass function predicted for a host halo simi [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p019_11.png]

Discussion (0). Continue with ORCID 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. Wide binaries in ultra-faint dwarf galaxies as a probe of extended dark objects

    hep-ph 2026-07 conditional novelty 5.0 of 10

    Wide binaries in Boötes I exclude dark-matter fractions down to ~10^-3 to 10^-2 for extended dark objects between 0.1 and 3000 solar masses with radii up to 10^7 solar radii, implying P_R ≲ 5×10^-6 at k ≈ 4×10^2-3×10^...

Reference graph

Works this paper leans on

118 extracted references · 85 linked inside Pith · cited by 1 Pith paper

  1. [1]

    The standard lore To go from the matter density contrast fieldδto the matter density fieldδ R averaged over some comoving scaleR, we resort to a filtering window function in real comoving space,W R — for the moment, we forget about the redshift or time dependence on purpose (it factors out, and will be recovered later on); all quantities are evaluated atz...

  2. [2]

    Such a description is perfectly fine to predict subhalo populations arising from the power-law part of the primordial power spectrum given in Eq

    Adding an UCMH component So far, we have discussed the canonical DM case, with the varianceSstemming from a given matter power spec- trumP m. Such a description is perfectly fine to predict subhalo populations arising from the power-law part of the primordial power spectrum given in Eq. (21). How- ever, there should be another population coming from the a...

  3. [3]

    compactness

    Basic tidal evolution of subhalos and UCMHs Since we have defined the subhalo mass function for both standard subhalos and UCMHs in a given host halo, we further need to specify how these objects are spa- tially distributed and evolve in their host halo, assumed spherically symmetric. Here, we will follow the semi- analytical approach developed in Refs. [...

  4. [4]

    P. J. E. Peebles, ApJL263, L1 (1982)

    1982

  5. [5]

    G. R. Blumenthal, S. M. Faber, J. R. Primack, and M. J. Rees, Nature (London)311, 517 (1984)

    1984

  6. [6]

    Ma and E

    C.-P. Ma and E. Bertschinger, Astrophys. J.455, 7 (1995), astro-ph/9506072

    arXiv 1995

  7. [7]

    W. H. Press and P. Schechter, Astrophys. J.187, 425 (1974)

    1974

  8. [8]

    J. M. Bardeen, J. R. Bond, N. Kaiser, and A. S. Szalay, Astrophys. J.304, 15 (1986)

    1986

Show all 118 references
  1. [9]

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

    1991

  2. [10]

    Lacey and S

    C. Lacey and S. Cole, MNRAS262, 627 (1993)

    1993

  3. [11]

    H. Mo, F. C. van den Bosch, and S. White,Galaxy Formation and Evolution(Cambridge University Press, 2010)

    2010

  4. [12]

    Vogelsberger, F

    M. Vogelsberger, F. Marinacci, P. Torrey, and E. Puchwein, Nature Reviews Physics2, 42 (2020), arXiv:1909.07976 [astro-ph.GA]

    2020 arXiv

  5. [13]

    Abdallaet al., Journal of High Energy Astrophysics 34, 49 (2022), arXiv:2203.06142 [astro-ph.CO]

    E. Abdallaet al., Journal of High Energy Astrophysics 34, 49 (2022), arXiv:2203.06142 [astro-ph.CO]

    2022 arXiv

  6. [14]

    P. J. E. Peebles, Annals of Physics447, 169159 (2022), arXiv:2208.05018 [astro-ph.CO]

    2022 arXiv

  7. [15]

    P. J. E. Peebles, Philosophical Transactions of the Royal Society of London Series A383, 20240021 (2025), arXiv:2405.18307 [astro-ph.CO]

    2025 arXiv

  8. [16]

    Baumann, arXiv e-prints , arXiv:0907.5424 (2009), arXiv:0907.5424 [hep-th]

    D. Baumann, arXiv e-prints , arXiv:0907.5424 (2009), arXiv:0907.5424 [hep-th]

    2009 arXiv

  9. [17]

    Ach´ ucarroet al., arXiv e-prints , arXiv:2203.08128 (2022), arXiv:2203.08128 [astro-ph.CO]

    A. Ach´ ucarroet al., arXiv e-prints , arXiv:2203.08128 (2022), arXiv:2203.08128 [astro-ph.CO]

    2022 arXiv

  10. [18]

    Cirelli, A

    M. Cirelli, A. Strumia, and J. Zupan, arXiv e-prints , arXiv:2406.01705 (2024), arXiv:2406.01705 [hep-ph]

    2024 arXiv

  11. [19]

    Hofmann, D

    S. Hofmann, D. J. Schwarz, and H. St¨ ocker, Phys. Rev. D64, 083507 (2001), arXiv:astro-ph/0104173 [astro- ph]

    2001 arXiv

  12. [20]

    A. M. Green, S. Hofmann, and D. J. Schwarz, J. Cosmol- ogy Astropart. Phys.8, 003 (2005), astro-ph/0503387

    2005 arXiv

  13. [21]

    Bringmann and S

    T. Bringmann and S. Hofmann, J. Cosmology As- tropart. Phys.4, 016 (2007), hep-ph/0612238

    2007 arXiv

  14. [22]

    D. J. E. Marsh, Phys. Rep.643, 1 (2016), arXiv:1510.07633

    2016 arXiv

  15. [23]

    Dodelson and L

    S. Dodelson and L. M. Widrow, Phys. Rev. Lett.72, 17 (1994), hep-ph/9303287

    1994 arXiv

  16. [24]

    Colombi, S

    S. Colombi, S. Dodelson, and L. M. Widrow, Astrophys. J.458, 1 (1996), astro-ph/9505029

    1996 arXiv

  17. [25]

    W. Hu, R. Barkana, and A. Gruzinov, Phys. Rev. Lett. 85, 1158 (2000), astro-ph/0003365

    2000 arXiv

  18. [26]

    E. G. M. Ferreira, The Astronomy and Astro- physics Review29, 10.1007/s00159-021-00135-6 (2020), arXiv:2005.03254 [astro-ph.CO]

    2020 doi arXiv

  19. [27]

    Zavala and C

    J. Zavala and C. S. Frenk, Galaxies7, 81 (2019), arXiv:1907.11775 [astro-ph.CO]

    2019 arXiv

  20. [28]

    Silk and A

    J. Silk and A. Stebbins, Astrophys. J.411, 439 (1993)

    1993

  21. [29]

    Diemand, M

    J. Diemand, M. Kuhlen, P. Madau, M. Zemp, B. Moore, D. Potter, and J. Stadel, Nature (London)454, 735 (2008), arXiv:0805.1244

    2008 arXiv

  22. [30]

    Springel, J

    V. Springel, J. Wang, M. Vogelsberger, A. Ludlow, A. Jenkins, A. Helmi, J. F. Navarro, C. S. Frenk, and S. D. M. White, MNRAS391, 1685 (2008), arXiv:0809.0898

    2008 arXiv

  23. [31]

    A. A. Starobinskii, Pisma v Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki55, 477 (1992)

    1992

  24. [32]

    Baumann and L

    D. Baumann and L. McAllister,Inflation and String Theory(Cambridge Monographs on Mathematical Physics, 2014) arXiv:1404.2601 [hep-th]

    2014 arXiv

  25. [33]

    Ballesteros and M

    G. Ballesteros and M. Taoso, Phys. Rev. D97, 023501 (2018), arXiv:1709.05565 [hep-ph]

    2018 arXiv

  26. [34]

    C. T. Byrnes, P. S. Cole, and S. P. Patil, J. Cosmology Astropart. Phys.2019, 028 (2019), arXiv:1811.11158 [astro-ph.CO]

    2019 arXiv

  27. [35]

    Franciolini, Y

    G. Franciolini, Y. Gouttenoire, and R. Jinno, Phys. Rev. Lett.136, 171404 (2026), arXiv:2503.01962 [hep-ph]

    2026 arXiv

  28. [36]

    B. J. Carr and S. W. Hawking, MNRAS168, 399 (1974)

    1974

  29. [37]

    G. F. Chapline, Nature (London)253, 251 (1975)

    1975

  30. [38]

    Carr and F

    B. Carr and F. K¨ uhnel, Annual Review of Nuclear 20 and Particle Science70, 355 (2020), arXiv:2006.02838 [astro-ph.CO]

    2020 arXiv

  31. [39]

    Berezinsky, V

    V. Berezinsky, V. Dokuchaev, and Y. Eroshenko, Phys. Rev. D68, 103003 (2003), astro-ph/0301551

    2003 arXiv

  32. [40]

    Ricotti and A

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

    2009 arXiv

  33. [41]

    Berezinsky, V

    V. Berezinsky, V. Dokuchaev, Y. Eroshenko, M. Kachel- rieß, and M. A. Solberg, Phys. Rev. D81, 103529 (2010), arXiv:1002.3444 [astro-ph.CO]

    2010 arXiv

  34. [42]

    V. S. Berezinsky, V. I. Dokuchaev, and Y. N. Eroshenko, J. Cosmology Astropart. Phys.12, 007 (2011), arXiv:1107.2751 [astro-ph.HE]

    2011 arXiv

  35. [43]

    V. S. Berezinsky, V. I. Dokuchaev, and Y. N. Eroshenko, Physics Uspekhi57, 1 (2014), arXiv:1405.2204 [astro- ph.HE]

    2014 arXiv

  36. [44]

    M. S. Delos, A. L. Erickcek, A. P. Bailey, and M. A. Alvarez, Phys. Rev. D98, 063527 (2018), arXiv:1806.07389

    2018 arXiv

  37. [45]

    M. S. Delos and J. Silk, MNRAS 10.1093/mn- ras/stad356 (2023), arXiv:2210.04904 [astro-ph.CO]

    2023 doi arXiv

  38. [46]

    C. G. Lacey and J. P. Ostriker, Astrophys. J.299, 633 (1985)

    1985

  39. [47]

    K. V. Johnston, D. N. Spergel, and C. Haydn, Astro- phys. J.570, 656 (2002), arXiv:astro-ph/0111196 [astro- ph]

    2002 arXiv

  40. [48]

    Pe˜ narrubia, A

    J. Pe˜ narrubia, A. D. Ludlow, J. Chanam´ e, and M. G. Walker, MNRAS461, L72 (2016), arXiv:1605.09384 [astro-ph.GA]

    2016 arXiv

  41. [49]

    Pe˜ narrubia, MNRAS474, 1482 (2018), arXiv:1710.06443

    J. Pe˜ narrubia, MNRAS474, 1482 (2018), arXiv:1710.06443

    2018 arXiv

  42. [50]

    B. T. Chiang, J. P. Ostriker, and H.-Y. Schive, MNRAS 518, 4045 (2023), arXiv:2211.07452 [astro-ph.GA]

    2023 arXiv

  43. [51]

    P. W. Graham, H. Ramani, and M. Ruhdorfer, Phys. Rev. D113, 023047 (2026), arXiv:2510.01310 [hep-ph]

    2026

  44. [52]

    Gilman, A

    D. Gilman, A. M. Nierenberg, T. Treu,et al., arXiv e-prints , arXiv:2606.05277 (2026), arXiv:2606.05277 [astro-ph.CO]

    2026 arXiv

  45. [53]

    Bringmann, D

    T. Bringmann, D. Croon, and S. Sevillano Mu˜ noz, arXiv e-prints , arXiv:2506.20704 (2025), arXiv:2506.20704 [astro-ph.CO]

    2025 arXiv

  46. [54]

    Ando, arXiv e-prints , arXiv:2603.04267 (2026), arXiv:2603.04267 [astro-ph.CO]

    S. Ando, arXiv e-prints , arXiv:2603.04267 (2026), arXiv:2603.04267 [astro-ph.CO]

    2026

  47. [55]

    J. A. Dror, H. Ramani, T. Trickle, and K. M. Zurek, Phys. Rev. D100, 023003 (2019), arXiv:1901.04490

    2019 arXiv

  48. [56]

    Benito, K

    M. Benito, K. Karchev, R. K. Leane, S. P˜ oder, J. Smirnov, and R. Trotta, J. Cosmology As- tropart. Phys.2024, 038 (2024), arXiv:2405.09578 [astro-ph.IM]

    2024 arXiv

  49. [57]

    Phoroutan-Mehr and T

    M. Phoroutan-Mehr and T. Fetherolf, Phys. Rev. D 112, 036012 (2025), arXiv:2503.00125 [hep-ph]

    2025 arXiv

  50. [58]

    C. Ilie, C. Levy, and J. Diks, J. Cosmology As- tropart. Phys.2024, 082 (2024), arXiv:2312.13979 [astro-ph.CO]

    2024 arXiv

  51. [59]

    B. V. Lehmann, A. Webber, O. G. Ross, and S. Pro- fumo, J. Cosmology Astropart. Phys.2022, 079 (2022), arXiv:2205.09756 [astro-ph.EP]

    2022 arXiv

  52. [60]

    Halpern, E

    P. Halpern, E. Cauley, M. Stoltzmann, and M. Wilshusen, arXiv e-prints , arXiv:2512.03118 (2025), arXiv:2512.03118 [gr-qc]

    2025

  53. [61]

    Penarrubia, S

    J. Penarrubia, S. E. Koposov, M. G. Walker, G. Gilmore, N. Wyn Evans, and C. D. Mackay, arXiv e- prints , arXiv:1005.5388 (2010), arXiv:1005.5388 [astro- ph.GA]

    2010 arXiv

  54. [62]

    E. D. Ramirez and M. R. Buckley, MNRAS525, 5813 (2023), 2209.08100

    2023 arXiv

  55. [63]

    Tyler, A

    E. Tyler, A. M. Green, and S. P. Goodwin, MNRAS 524, 3052 (2023), arXiv:2207.08668 [astro-ph.GA]

    2023 arXiv

  56. [64]

    Shariat, K

    C. Shariat, K. El-Badry, M. Gennaro, K. Ding, J. D. Si- mon,et al., PASP137, 104103 (2025), arXiv:2509.04555 [astro-ph.GA]

    2025

  57. [65]

    Bhalla, B

    B. Bhalla, B. V. Lehmann, K. Sinha, and T. Xu, Phys. Rev. D111, 043029 (2025), arXiv:2408.04697 [hep-ph]

    2025 arXiv

  58. [66]

    Crida, Comptes Rendus

    A. Crida, Comptes Rendus. Physique24, 233 (2023)

    2023

  59. [67]

    Mordasini, Planetary population synthesis, inHand- book of Exoplanets, edited by H

    C. Mordasini, Planetary population synthesis, inHand- book of Exoplanets, edited by H. J. Deeg and J. A. Bel- monte (Springer International Publishing, Cham, 2018) pp. 2425–2474

    2018

  60. [68]

    H. J. Deeg and J. A. Belmonte, eds.,Handbook of Exo- planets, 2nd ed. (Springer Cham, 2026)

    2026

  61. [69]

    N. R. Deacon, M. C. Liu, E. A. Magnier,et al., Astro- phys. J.792, 119 (2014), arXiv:1407.2938 [astro-ph.SR]

    2014 arXiv

  62. [70]

    Zhang, M

    Z. Zhang, M. C. Liu, Z. R. Claytor, W. M. J. Best, T. J. Dupuy, and R. J. Siverd, ApJL916, L11 (2021), arXiv:2107.02805 [astro-ph.EP]

    2021 arXiv

  63. [71]

    Rothermichet al., AJ167, 253 (2024), arXiv:2403.04592 [astro-ph.SR]

    A. Rothermichet al., AJ167, 253 (2024), arXiv:2403.04592 [astro-ph.SR]

    2024 arXiv

  64. [72]

    Cifuentes, J

    C. Cifuentes, J. A. Caballero, J. Gonz´ alez-Payo, et al., A&A693, A228 (2025), arXiv:2412.12264 [astro- ph.SR]

    2025 arXiv

  65. [73]

    Binney and S

    J. Binney and S. Tremaine,Galactic Dynamics, 2nd ed., Princeton series in astrophysics (Princeton University Press, Princeton, NJ USA, 2008., 2008)

    2008

  66. [74]

    Facchinetti, M

    G. Facchinetti, M. Stref, and J. Lavalle, arXiv e-prints , arXiv:2201.09788 (2022), arXiv:2201.09788 [astro- ph.GA]

    2022 arXiv

  67. [75]

    O. E. Gerhard and S. M. Fall, MNRAS203, 1253 (1983)

    1983

  68. [76]

    Stref and J

    M. Stref and J. Lavalle, Phys. Rev. D95, 063003 (2017), arXiv:1610.02233

    2017 arXiv

  69. [77]

    G. F. Abell´ an and G. Facchinetti, J. Cosmology As- tropart. Phys.2023, 032 (2023), arXiv:2304.02996 [astro-ph.CO]

    2023 arXiv

  70. [78]

    The Planck Collaborationet al., A&A641, A6 (2020), arXiv:1807.06209 [astro-ph.CO]

    2020 arXiv

  71. [79]

    S. Bird, H. V. Peiris, M. Viel, and L. Verde, MNRAS 413, 1717 (2011), arXiv:1010.1519 [astro-ph.CO]

    2011 arXiv

  72. [80]

    Chluba, A

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

    2012 arXiv

  73. [81]

    Inomata and T

    K. Inomata and T. Nakama, Phys. Rev. D99, 043511 (2019), arXiv:1812.00674 [astro-ph.CO]

    2019 arXiv

  74. [82]

    Binney,Stellar dynamics for physicists(Indepen- dently published, 2026)

    J. Binney,Stellar dynamics for physicists(Indepen- dently published, 2026)

    2026

  75. [83]

    Spergelet al., arXiv e-prints , arXiv:1503.03757 (2015), arXiv:1503.03757 [astro-ph.IM]

    D. Spergelet al., arXiv e-prints , arXiv:1503.03757 (2015), arXiv:1503.03757 [astro-ph.IM]

    2015 arXiv

  76. [84]

    Chauvin, Comptes Rendus

    G. Chauvin, Comptes Rendus. Physique24, 129 (2023)

    2023

  77. [85]

    S. Cole, C. G. Lacey, C. M. Baugh, and C. S. Frenk, MN- RAS319, 168 (2000), arXiv:astro-ph/0007281 [astro- ph]

    2000 arXiv

  78. [86]

    Parkinson, S

    H. Parkinson, S. Cole, and J. Helly, MNRAS383, 557 (2008), arXiv:0708.1382

    2008 arXiv

  79. [87]

    A. J. Benson, New A17, 175 (2012), arXiv:1008.1786

    2012 arXiv

  80. [88]

    Jiang, A

    F. Jiang, A. Dekel, J. Freundlich, F. C. van den Bosch, S. B. Green, P. F. Hopkins, A. Benson, and X. Du, arXiv e-prints , arXiv:2005.05974 (2020), arXiv:2005.05974 [astro-ph.GA]

    2005 arXiv

  81. [89]

    Hiroshima, S

    N. Hiroshima, S. Ando, and T. Ishiyama, MNRAS 517, arXiv:2206.01358 (2022), arXiv:2206.01358 [astro- ph.CO]. 21

    2022 arXiv

  82. [90]

    A. R. Zentner, International Journal of Modern Physics D16, 763 (2007), astro-ph/0611454

    2007 arXiv

  83. [91]

    Dodelson,Modern Cosmology(Academic Press, 2003)

    S. Dodelson,Modern Cosmology(Academic Press, 2003)

    2003

  84. [92]

    D. J. Heath, MNRAS179, 351 (1977)

    1977

  85. [93]

    S. M. Carroll, W. H. Press, and E. L. Turner, ARA&A 30, 499 (1992)

    1992

  86. [94]

    D. J. Eisenstein and W. Hu, Astrophys. J.496, 605 (1998), astro-ph/9709112

    1998 arXiv

  87. [95]

    R. K. Sheth and G. Tormen, MNRAS308, 119 (1999), astro-ph/9901122

    1999 arXiv

  88. [96]

    R. K. Sheth, H. J. Mo, and G. Tormen, MNRAS323, 1 (2001), astro-ph/9907024

    2001 arXiv

  89. [97]

    S. Cole, J. Helly, C. S. Frenk, and H. Parkinson, MN- RAS383, 546 (2008), arXiv:0708.1376 [astro-ph]

    2008 arXiv

  90. [98]

    Cole, Astrophys

    S. Cole, Astrophys. J.367, 45 (1991)

    1991

  91. [99]

    R. S. Somerville and J. R. Primack, MNRAS310, 1087 (1999), arXiv:astro-ph/9802268 [astro-ph]

    1999 arXiv

  92. [100]

    Jiang and F

    F. Jiang and F. C. van den Bosch, MNRAS440, 193 (2014), arXiv:1311.5225 [astro-ph.CO]

    2014 arXiv

  93. [101]

    X. Yang, H. J. Mo, Y. Zhang, and F. C. van den Bosch, Astrophys. J.741, 13 (2011), arXiv:1104.1757

    2011 arXiv

  94. [102]

    H¨ utten, M

    M. H¨ utten, M. Stref, C. Combet, J. Lavalle, and D. Maurin, Galaxies7, 60 (2019), arXiv:1904.10935 [astro-ph.HE]

    2019 arXiv

  95. [103]

    P. J. McMillan, MNRAS465, 76 (2017), arXiv:1608.00971

    2017 arXiv

  96. [104]

    Zhao, MNRAS278, 488 (1996), astro-ph/9509122

    H. Zhao, MNRAS278, 488 (1996), astro-ph/9509122

    1996 arXiv

  97. [105]

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

    1996 arXiv

  98. [106]

    F. C. van den Bosch and G. Ogiya, MNRAS475, 4066 (2018), arXiv:1801.05427

    2018 arXiv

  99. [107]

    F. C. van den Bosch, G. Ogiya, O. Hahn, and A. Burk- ert, MNRAS474, 3043 (2018), arXiv:1711.05276 [astro- ph.GA]

    2018 arXiv

  100. [108]

    Errani and J

    R. Errani and J. Pe˜ narrubia, MNRAS491, 4591 (2020), arXiv:1906.01642

    2020 arXiv

  101. [109]

    Tormen, A

    G. Tormen, A. Diaferio, and D. Syer, MNRAS299, 728 (1998), astro-ph/9712222

    1998 arXiv

  102. [110]

    Hayashi, J

    E. Hayashi, J. F. Navarro, J. E. Taylor, J. Stadel, and T. Quinn, Astrophys. J.584, 541 (2003), astro- ph/0203004

    2003

  103. [111]

    Diemand, B

    J. Diemand, B. Moore, and J. Stadel, MNRAS352, 535 (2004), astro-ph/0402160

    2004 arXiv

  104. [112]

    F. C. van den Bosch, MNRAS468, 885 (2017), arXiv:1611.02657

    2017 arXiv

  105. [113]

    Moore, F

    B. Moore, F. Governato, T. Quinn, J. Stadel, and G. Lake, ApJL499, L5 (1998), astro-ph/9709051

    1998 arXiv

  106. [114]

    M. S. Delos, A. L. Erickcek, A. P. Bailey, and M. A. Alvarez, Phys. Rev. D97, 041303 (2018), arXiv:1712.05421

    2018 arXiv

  107. [115]

    Aumer, J

    M. Aumer, J. Binney, and R. Sch¨ onrich, MNRAS462, 1697 (2016), arXiv:1607.01972 [astro-ph.GA]

    2016 arXiv

  108. [116]

    Zurlo, inEncyclopedia of Astrophysics, Volume 1, Vol

    A. Zurlo, inEncyclopedia of Astrophysics, Volume 1, Vol. 1 (2026) pp. 395–418, arXiv:2404.05797 [astro- ph.EP]

    2026 arXiv

  109. [117]

    E. E. Salpeter, Astrophys. J.121, 161 (1955)

    1955

  110. [118]

    B. W. Carroll and D. A. Ostlie,An introduction to mod- ern astrophysics, 2nd ed. (Cambridge University Press, 2017)

    2017

Pith tools

Reviewed July 12, 2026 · model on record in the stance chip above.