Pith. sign in

REVIEW 3 major objections 4 minor 77 references

Comparing the Spatial Correlation of Binary Black Hole Mergers to Large-Scale Structure through the Illustris Simulation

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

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

Pith's one-line read The paper claims that massive black hole mergers in the LISA mass range cluster more strongly than galaxies at scales below 10 Mpc/h, with a bias that stays nearly flat across redshift, so LISA could trace large-scale structure through…

desk verdict A useful new simulation measurement of LISA-mass MBBH clustering, but the flat-bias conclusion is undercut by internally inconsistent slope values. read the letter →

arxiv 2507.11813 v1 pith:DDPTJMP7 submitted 2025-07-16 astro-ph.CO

Shaniya Jarrett , Kelly Holley-Bockelmann , Robert J. Scherrer This is my paper
classification astro-ph.CO
keywords gravitationalwavesLISAmassivebinaryblackholeslarge-scalestructuretwo-pointcorrelationfunctionclusteringbiasIllustrissimulationcosmologicalhydrodynamic
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 tries to establish that massive black hole mergers in the LISA band are more strongly clustered than galaxies at scales below about 10 Mpc per $h$, and that the merger-to-galaxy bias stays roughly constant with separation from $z=0$ to $z=2$. If correct, LISA's detected mergers would trace the same large-scale structure shape as galaxies, giving an independent gravitational-wave-based tracer of cosmic structure and a simple way to subtract the massive-black-hole foreground from the stochastic gravitational-wave background. The case is made with the Illustris-3 simulation by measuring two-point correlation functions of about 6500 synthetic mergers and hundreds of thousands of galaxies in four redshift bins. The main caveat is that the simulation defines a merger as two black hole particles entering a 1 kpc softening radius, skipping the long inspiral that LISA would actually observe.

What carries the argument

The central machinery is the two-point correlation function $\xi(r)$, computed with the Landy--Szalay estimator and a pair-counting code, and the bias ratio $\xi_{\rm merger}(r)/\xi_{\rm galaxy}(r)$. The merger sample consists of black hole pairs that come within the 1 kpc softening length in the mass range $2.84\times10^5$ to $10^8\,M_\odot$, while galaxies are selected by stellar mass $10^9$--$10^{12.5}\,M_\odot$. The flatness of the bias ratio across separation is the load-bearing result: a scale-independent bias means a single multiplicative factor connects merger clustering to galaxy clustering.

What would settle it

Compute the merger-galaxy clustering bias in a simulation that resolves the 1 kpc-to-coalescence inspiral, including dynamical friction, gas interactions, and gravitational radiation delay; if the bias becomes scale-dependent below 10 Mpc $h^{-1}$ or the excess clustering disappears, the paper's central claim is contradicted.

Watch

Extended reading notes

Core claim

The authors report that in the Illustris-3 simulation, massive binary black hole mergers are more strongly clustered than galaxies at every redshift from $z=0$ to $z=2$, most clearly below about $10\,h^{-1}\mathrm{Mpc}$ and most prominently at $z=0.85$--$2$, where the merger-to-galaxy bias ratio exceeds 2. The two-point correlation functions follow power laws with slopes $\gamma_m=2.0$--$2.28$ for mergers and $\gamma_g=2.03$--$2.07$ for galaxies, and the bias stays nearly flat with separation. They take this as evidence that LISA-detectable massive black hole mergers trace the same large-scale structure as galaxies, so a galaxy survey can act as a proxy for merger locations and as a prior for subtracting the massive-black-hole foreground from the stochastic gravitational-wave background.

Load-bearing premise

The simulation defines a merger as two black holes coming within 1 kpc of each other, skipping the long inspiral and dynamical-friction phase that determines whether LISA actually sees the event, so the simulated merger environments may not match the real LISA source population.

Editorial extensions

If this is right

  • A LISA massive-black-hole merger catalog would trace the shape of the galaxy correlation function, so galaxy surveys can provide a one-parameter prior for merger clustering.
  • Subtracting the massive-black-hole foreground from the stochastic gravitational-wave background can be done with a scale-independent bias rather than a separate bias model at every separation.
  • At $z=0.85$--$2$, mergers preferentially sample overdense environments, so their clustering can be used to study structure formation near cosmic noon.
  • Massive black hole mergers detected by LISA could act as an independent large-scale structure tracer that is free of electromagnetic selection bias.

Reading between the lines

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

  • Editorial inference: because LISA's sky localization is coarse, the practical route may be to cross-correlate MBBH events with galaxy maps rather than measure their autocorrelation; the flat bias derived here would keep that cross-correlation interpretable with a single multiplicative factor.
  • Editorial inference: a natural next test is to repeat the measurement in a larger-volume simulation or one with resolved inspiral delays to see whether the flat bias survives on scales above 20 Mpc/$h$, where the 75 Mpc/$h$ Illustris-3 box cannot constrain it.
  • Editorial inference: if the flat bias persists, the minimum number of LISA events needed to detect the correlation becomes a key quantity; the roughly 1600 mergers per redshift bin and 12.8% fractional uncertainty in this paper suggest comparable or larger real catalogs will be needed.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper compares the two-point correlation functions of massive binary black hole (MBBH) mergers and galaxies in the Illustris-3 simulation, using the Landy-Szalay estimator with bootstrap uncertainties across four redshift bins from z=0 to z=2. The authors report that MBBH mergers are more strongly clustered than galaxies at small scales, that the merger-to-galaxy bias is relatively flat as a function of separation, and that this behavior supports using LISA-detected MBBH mergers as tracers of large-scale structure and as a prior for foreground subtraction from the stochastic gravitational-wave background.

Significance. If the central result holds, this is a useful first step toward connecting LISA-visible MBBH mergers with large-scale structure. The paper has clear strengths: it uses a standard, well-tested estimator (Landy-Szalay via Corrfunc), draws directly on an external simulation rather than deriving the conclusion from the assumed model, reports bootstrap confidence intervals for the correlation functions, and explicitly acknowledges the merger-definition limitations in Section 4. However, the quantitative support for the flat-bias conclusion is currently undermined by internally inconsistent power-law slopes and by the absence of uncertainties or a flatness test for the bias ratio, so the manuscript needs substantial revision before the central claim can be accepted.

major comments (3)
  1. [Sections 3 and 5] The reported power-law slopes for the z=0.85-2.0 bin are irreconcilable: Section 3 gives gamma_m=2.06 and gamma_g=2.03, while Section 5 gives gamma_m=2.28 and gamma_g=2.03 for the same bin. This is not merely a typographical nuisance: if gamma_m=2.28 while gamma_g=2.03, then b(r)=xi_m/xi_g scales as r^{-0.25} over the fitted range, which directly contradicts the flat-bias conclusion; if Section 3 is correct, the Conclusion is wrong. The authors must state which values are correct, re-fit if necessary, and report all slopes consistently before the flat-bias claim can be evaluated.
  2. [Section 3, Figure 2] Figure 2, which carries the central flat-bias claim, shows the merger-to-galaxy ratio with no error bars and no quantitative flatness test. The bootstrap uncertainties shown for the correlation functions in Figure 1 should be propagated into the ratio, or the flatness should be assessed with a fit and a quoted statistic; without this, the statement that the bias is 'relatively constant' is only a visual impression, and the text itself notes large fluctuations for r > 10 Mpc/h.
  3. [Section 2.2 and Section 4] The merger definition (two black holes coming within the 1 kpc softening length, without post-dynamical-friction inspiral, gas-disk interaction, or gravitational-radiation delay) is acknowledged as a caveat in Section 4, but it is load-bearing for the LISA implications: if the omitted post-softening evolution preferentially moves binaries out of dense environments, the simulated MBBH clustering will not transfer to true LISA sources. I ask that the authors either add a sensitivity check, for example by assigning delayed merger positions with a physically motivated waiting-time prescription, or explicitly restrict the foreground-subtraction and LSS-tracer conclusions to mergers as defined in Illustris-3 rather than to LISA-observable MBBHs.
minor comments (4)
  1. [Sections 3 and 4] The galaxy slope is labeled gamma_m in two places where gamma_g is clearly intended: Section 3 states the slopes of 'both MBBH mergers and galaxies' as 'gamma_m = 2.03-2.07, and gamma_m = 2.0-2.28', and Section 4 similarly says galaxy slopes 'ranged from gamma_m = 2.03-2.07'; these labels should be corrected to avoid ambiguity.
  2. [Section 2.3] The text says the bins 'range from 1 to 30 Mpc h^{-1}' and also that 'rmax up to 20 Mpc h^{-1}' is used to minimize edge effects; this is confusing and should be reconciled in a single clear statement of the binning.
  3. [Section 3] The statement that the power-law slope 'increases with time' is not supported by the quoted values (merger slopes 2.28, 2.0, 2.1, 2.06 across the four bins), so the trend description should be corrected or quantified.
  4. [Section 3 and Figure 1 caption] The prose overclaims 'all scales' when the same section describes the robust signal as below roughly 10-15 Mpc/h and attributes larger-scale behavior to noise and edge effects; the claims should be qualified to the scales where the measurement is statistically reliable.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the clustering comparison is a direct measurement from an external simulation, with no fitted parameter or self-citation chain doing the work of the central claim.

full rationale

The paper's central claim is that MBBH mergers in Illustris-3 cluster more strongly than galaxies at scales below 10 Mpc/h and that the merger-to-galaxy bias is relatively flat. This claim is established by directly measuring two-point correlation functions from an external, publicly available simulation and taking their ratio. No parameter is fitted to the data and then renamed as a prediction; the power-law slopes reported in Section 3 are descriptive characterizations of the measured correlation functions, and the bias is simply the ratio xi_m(r)/xi_g(r). The merger population is defined by the simulation's own 1 kpc softening-length rule, and the paper explicitly acknowledges the omission of post-dynamical-friction inspiral and gravitational radiation delays in Section 4. These caveats affect the astrophysical interpretation of the results, but they do not make the measurement circular. The paper's self-citations, e.g., to Sijacki et al. (2015) for the merger definition and to the authors' own earlier work on BH dynamics, are used contextually rather than as the load-bearing evidence for the clustering claim. No uniqueness theorem or prior result by the same authors is invoked to forbid alternatives. One noteworthy correctness issue is an internal inconsistency in the reported slopes: Section 3 gives gamma_m = 2.28 for the z = 0-0.20 bin while Section 3 also reports gamma_g = 2.07, implying a scale-dependent bias of b(r) proportional to r^(gamma_g - gamma_m), and the Conclusion quotes gamma_m = 2.28 for the z = 0.85-2.0 bin that Section 3 reported as gamma_m = 2.06. This inconsistency undermines the flat-bias claim and should be corrected, but it is a consistency/correctness problem, not a circularity problem. The analysis is self-contained against an external simulation and does not reduce to its own inputs.

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

The analysis leans on the Illustris simulation's subgrid model and on the merger definition as primary assumptions, plus the standard correlation estimator and bootstrap uncertainties. The fitted power-law slopes are descriptive and not load-bearing. No new physical entities are introduced.

free parameters (4)
  • MBBH merger 2pt CF power-law slope gamma_m = 2.0 to 2.28 depending on redshift bin
    Fitted to the measured merger correlation function in each redshift bin; values are reported inconsistently in Sections 3, 4, and 5.
  • Galaxy 2pt CF power-law slope gamma_g = 2.03 to 2.07 depending on redshift bin
    Fitted to the measured galaxy correlation function; used for comparison with the merger slope.
  • Redshift bin boundaries = 0.0, 0.20, 0.46, 0.85, 2.0
    Chosen by hand to balance the number of mergers per bin (~1600), which directly shapes the statistical comparison.
  • Correlation function binning = 20 log-spaced bins over roughly 1 to 30 Mpc/h with r_max 20 Mpc/h
    Chosen based on Corrfunc recommendations; affects the measured shape and edge corrections.
assumptions (4)
  • domain assumption Illustris subgrid prescriptions for star formation, gas cooling, and black hole feedback produce a realistic population of galaxies and merging massive black holes.
    Used throughout Sections 2.1 and 2.2 as the simulated universe on which all measurements are made; known to be calibration-dependent.
  • domain assumption Mergers are counted when two black holes come within the 1 kpc softening length, with no dynamical friction, inspiral, or gravitational radiation delay.
    Section 2.2 defines the merger criterion and notes the separation is about a billion times larger than the true merger; the authors concede this omission in Section 4.
  • standard math Landy-Szalay estimator with a random catalog of comparable density correctly corrects for survey volume and edge effects in a 75 Mpc/h periodic box.
    Stated as the correlation function method in Section 2.3; standard in the field but not validated for the small merger sample here.
  • domain assumption Bootstrap resampling gives valid confidence intervals for correlation functions computed from a few thousand merger pairs.
    Confidence intervals in Figure 1 are derived from bootstrapping; no details on resampling scheme or pair-count correlation treatment are given.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Comparing the Spatial Correlation of Binary Black Hole Mergers to Large-Scale Structure through the Illustris Simulation." pith.science (2026). https://pith.science/paper/DDPTJMP7

@misc{pith2026250711813,
  author       = {Pith},
  title        = {Pith review of: Comparing the Spatial Correlation of Binary Black Hole Mergers to Large-Scale Structure through the Illustris Simulation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DDPTJMP7}},
  note         = {Machine review of arXiv:2507.11813}
}
abstract

Gravitational waves (GWs) have provided a new lens through which to view the universe beyond traditional electromagnetic methods. The upcoming space-based gravitational wave mission, Laser Interferometer Space Antenna (LISA), will give us the first glimpse of the sky in mHz gravitational waves, a waveband that contains a rich variety of sources including massive binary black hole (MBBH) mergers. In this work, we investigate the spatial distribution of MBBH mergers versus the galaxy distribution to determine how well LISA could be used as a unique and independent probe of large-scale structure. We compare the two-point correlation function (2pt CF) of MBBH mergers to that of galaxies within the cosmological hydrodynamic simulation IllustrisTNG. Our results show that MBBH mergers exhibit stronger clustering than galaxies at scales less than 10 Mpc $h^{-1}$, particularly at higher redshifts, and that the bias is relatively constant as a function of separation. These findings imply that the spatial distribution of MBBH mergers detectable by LISA could inform the observed galaxy distribution. In addition, this implies that searches for a cosmological background in LISA data could use a prior derived from large-scale structure observations to subtract the MBBH foreground.

Figures

Figures reproduced from arXiv: 2507.11813 by the authors.

Figure 1
Figure 1. The 2pt CF of MBBH mergers (blue) and galaxies (red) in Illustris-3 at redshifts z = 0 − 0.20, z = 0.20 − 0.46, z = 0.46−0.85, z = 0.85−2.0. We see that both MBBH mergers and galaxies are more clustered at smaller scales (< 5 Mpc h −1 ), and that MBBH mergers consistently exhibit stronger clustering compared to galaxies for all scales, particularly for higher redshift ranges. up to 20 Mpc h −1 to minimize edge effec… view at source ↗
Figure 2
Figure 2. The 2pt CF bias for MBBH mergers versus galaxies (purple) at redshifts z = 0−0.20, z = 0.20−0.46, z = 0.46−0.85, z = 0.85 − 2.0. For all redshift ranges, the bias remains relatively consistent at scales below 15 Mpc h −1 with more variation at larger distances. There is a slight increase in the ratio observed at higher redshifts. For redshift range z = 0.46 − 0.85, MBBH mergers continue to show higher clustering str… view at source ↗

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

77 extracted references · 22 canonical work pages

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address archivePrefix author booktitle chapter doi edition editor eprint howpublished institution journal key month number organization pages publisher school series title misctitle type volume year version url label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts ...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION format.url url empty "" new.block "" url * "" * if FUNCTION format.eprint eprint empty "" archivePrefix empty "" archivePrefix "arXiv" = new.block " " eprint * " " * new.block " " eprint * " " * if if if FUNCTION format.doi doi empty "" " " doi * " " * if FUNCTION format.pid doi empty eprint empty ur...

  3. [4]

    P., Abbott, R., Abbott, T

    Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2016, Physical Review Letters, 116, 061102, 10.1103/PhysRevLett.116.061102

    doi:10.1103/physrevlett.116.061102 2016

  4. [5]

    P., Abbott, R., Abbott, T

    Abbott, B. P., Abbott, R., Abbott, T. D., & Abraham, S. 2019, Phys. Rev. X, 9, 031040, 10.1103/PhysRevX.9.031040

    doi:10.1103/physrevx.9.031040 2019

  5. [6]

    2020, Astronomy & Astrophysics, 641, A6, 10.1051/0004-6361/201833910

    Aghanim, N., Akrami, Y., Ashdown, M., et al. 2020, Astronomy & Astrophysics, 641, A6, 10.1051/0004-6361/201833910

    doi:10.1051/0004-6361/201833910 2020

  6. [7]

    A., Almeida, A., et al

    Ahumada, R., Prieto, C. A., Almeida, A., et al. 2020, The Astrophysical Journal Supplement Series, 249, 3, 10.3847/1538-4365/ab929e

    doi:10.3847/1538-4365/ab929e 2020

  7. [8]

    2023, Living Reviews in Relativity, 26, 10.1007/s41114-022-00041-y

    Amaro-Seoane, P., Andrews, J., Arca Sedda, M., et al. 2023, Living Reviews in Relativity, 26, 10.1007/s41114-022-00041-y

    doi:10.1007/s41114-022-00041-y 2023

  8. [9]

    2017, Phys

    Amendola, L., Menegoni, E., Di Porto, C., Corsi, M., & Branchini, E. 2017, Phys. Rev. D, 95, 023505, 10.1103/PhysRevD.95.023505

    work page doi:10.1103/physrevd.95.023505 2017

Show all 77 references
  1. [10]

    2020, Physical Review D, 102, 063007, 10.1103/PhysRevD.102.063007

    Banagiri, S., Yunes, N., Thrane, E., & Isi, M. 2020, Physical Review D, 102, 063007, 10.1103/PhysRevD.102.063007

    2020 doi

  2. [11]

    2022, Monthly Notices of the Royal Astronomical Society, 506, 116–129, 10.1093/mnras/stac831

    Banks, S., Lee, K., Azimi, N., et al. 2022, Monthly Notices of the Royal Astronomical Society, 506, 116–129, 10.1093/mnras/stac831

    2022 doi

  3. [12]

    2004, Monthly Notices of the Royal Astronomical Society, 349, 882, 10.1111/j.1365-2966.2004.07509.x

    Basilakos, S., & Plionis, M. 2004, Monthly Notices of the Royal Astronomical Society, 349, 882, 10.1111/j.1365-2966.2004.07509.x

    2004

  4. [13]

    C., Volonteri, M., & Rees, M

    Begelman, M. C., Volonteri, M., & Rees, M. J. 2006, Monthly Notices of the Royal Astronomical Society, 370, 289, 10.1111/j.1365-2966.2006.10467.x

    2006

  5. [14]

    R., Bershady, M

    Blanton, M. R., Bershady, M. A., Abolfathi, B., Albareti, F. D., & Prieto, A. 2017, The Astronomical Journal, 154, 28, 10.3847/1538-3881/aa7567

    2017 doi

  6. [15]

    2023, Monthly Notices of the Royal Astronomical Society, 524, 2579, 10.1093/mnras/stad1097

    Bose, S., Hadzhiyska, B., Barrera, M., et al. 2023, Monthly Notices of the Royal Astronomical Society, 524, 2579, 10.1093/mnras/stad1097

    2023 doi

  7. [16]

    2021, Astronomy & Astrophysics, 646, A40, 10.1051/0004-6361/202039603

    Breton, M.-A., & de la Torre, S. 2021, Astronomy & Astrophysics, 646, A40, 10.1051/0004-6361/202039603

    2021 doi

  8. [17]

    2003, The Astrophysical Journal, 596, 34, 10.1086/377529

    Bromm, V., & Loeb, A. 2003, The Astrophysical Journal, 596, 34, 10.1086/377529

    2003 doi

  9. [18]

    2022, Monthly Notices of the Royal Astronomical Society, 510, 531, 10.1093/mnras/stab3411

    Chen, N., Ni, Y., Tremmel, M., et al. 2022, Monthly Notices of the Royal Astronomical Society, 510, 531, 10.1093/mnras/stab3411

    2022 doi

  10. [20]

    Collaboration, P., Ade, P. A. R., Aghanim, N., et al. 2016, Astronomy & Astrophysics, 594, A13, 10.1051/0004-6361/201525830

    2016 doi

  11. [21]

    2024, LISA Definition Study Report

    Colpi, M., Danzmann, K., Hewitson, M., et al. 2024, LISA Definition Study Report. 2402.07571

    2024 arXiv

  12. [22]

    1983, ApJ, 267, 465

    Davis, M., & Peebles, P. 1983, ApJ, 267, 465

    1983

  13. [23]

    2020, Monthly Notices of the Royal Astronomical Society, 491, 4973, 10.1093/mnras/stz3309

    DeGraf, C., & Sijacki, D. 2020, Monthly Notices of the Royal Astronomical Society, 491, 4973, 10.1093/mnras/stz3309

    2020 doi

  14. [24]

    2018, Physics Reports, 733, 1, 10.1016/j.physrep.2017.12.002

    Desjacques, V., Jeong, D., & Schmidt, F. 2018, Physics Reports, 733, 1, 10.1016/j.physrep.2017.12.002

    2018 doi

  15. [25]

    L., Allam, S., & Way, M

    Doroshkevich, A., Tucker, D. L., Allam, S., & Way, M. J. 2004, Astronomy & Astrophysics, 418, 7, 10.1051/0004-6361:20031780

    2004 doi

  16. [26]

    1916, Sitzungsber

    Einstein, A. 1916, Sitzungsber. Preuss. Akad. Wiss., 1, 688

    1916

  17. [27]

    J., Zehavi, I., Hogg, D

    Eisenstein, D. J., Zehavi, I., Hogg, D. W., et al. 2005, The Astrophysical Journal, 633, 560, 10.1086/466512

    2005 doi

  18. [28]

    2024, 10.48550/arXiv.2409.02194

    Fontanot, F., De Lucia, G., Xie, L., et al. 2024, 10.48550/arXiv.2409.02194

    2024 doi arXiv

  19. [29]

    1991, Physica Scripta, T36, 70, 10.1088/0031-8949/1991/T36/008

    Frenk, C. 1991, Physica Scripta, T36, 70, 10.1088/0031-8949/1991/T36/008

    1991 doi

  20. [30]

    1989, Science, 246, 897

    Geller, M., & Huchra, J. 1989, Science, 246, 897

    1989

  21. [31]

    1993, Mon

    Haehnelt, M., & Rees, M. 1993, Mon. Not. R. Astron. Soc., 263, 168, 10.1093/mnras/263.1.168

    1993 doi

  22. [32]

    Hamilton, A. J. S. 1988, The Astrophysical Journal, 331, L59, 10.1086/185257

    1988 doi

  23. [33]

    2019, Astronomy & Astrophysics, 626, A47, 10.1051/0004-6361/201833771

    Haslbauer, M., Dabringhausen, J., Kroupa, P., Javanmardi, B., & Banik, I. 2019, Astronomy & Astrophysics, 626, A47, 10.1051/0004-6361/201833771

    2019 doi

  24. [34]

    2003, Monthly Notices of the Royal Astronomical Society, 346, 78, 10.1046/j.1365-2966.2003.07063.x

    Hawkins, E., Maddox, S., Cole, S., et al. 2003, Monthly Notices of the Royal Astronomical Society, 346, 78, 10.1046/j.1365-2966.2003.07063.x

    2003

  25. [35]

    Holley-Bockelmann, K., Micic, M., Sigurdsson, S., & Rubbo, L. J. 2010, The Astrophysical Journal, 713, 1016, 10.1088/0004-637X/713/2/1016

    2010 doi

  26. [36]

    1926, ApJ, 64, 321

    Hubble, E. 1926, ApJ, 64, 321

    1926

  27. [37]

    2018, Illustris Simulation

    Illustris Collaboration . 2018, Illustris Simulation. https://www.illustris-project.org

    2018

  28. [38]

    2023, Monthly Notices of the Royal Astronomical Society, 519, 2083, 10.1093/mnras/stac3677

    Izquierdo-Villalba, D., Sesana, A., & Colpi, M. 2023, Monthly Notices of the Royal Astronomical Society, 519, 2083, 10.1093/mnras/stac3677

    2023 doi

  29. [39]

    1984, The Astrophysical Journal, 284, L9, 10.1086/184341

    Kaiser, N. 1984, The Astrophysical Journal, 284, L9, 10.1086/184341

    1984 doi

  30. [40]

    2024, arXiv e-prints, arXiv:2406.02504, 10.48550/arXiv.2406.02504

    K \"a rcher , M., Bel , J., & de la Torre , S. 2024, arXiv e-prints, arXiv:2406.02504, 10.48550/arXiv.2406.02504

    2024 doi arXiv

  31. [41]

    M., & Holley-Bockelmann, K

    Khan, F. M., & Holley-Bockelmann, K. 2021, Mon. Not. R. Astron. Soc., 508, 1174, 10.1093/mnras/stab2646

    2021 doi

  32. [42]

    M., Javed, F., Holley-Bockelmann, K., et al

    Khan, F. M., Javed, F., Holley-Bockelmann, K., et al. 2024, Astrophys. J., 976, 22, 10.3847/1538-4357/ad8082

    2024 doi

  33. [43]

    Kumar, S., Vijaykumar, A., & Nitz, A. H. 2022, The Astrophysical Journal, 930, 113, 10.3847/1538-4357/ac5e34

    2022 doi

  34. [44]

    1993, ApJ, 412, 64–71

    Landy, S., & Szalay, A. 1993, ApJ, 412, 64–71

    1993

  35. [45]

    2024, Monthly Notices of the Royal Astronomical Society, 000, 10.48550/arXiv.2409.06527

    Langen, V., Tamanini, N., Marsat, S., & Bortolas, E. 2024, Monthly Notices of the Royal Astronomical Society, 000, 10.48550/arXiv.2409.06527

    2024 doi arXiv

  36. [46]

    R., & Bonetti, M

    Li, K., Bogdanović, T., Ballantyne, D. R., & Bonetti, M. 2022, The Astrophysical Journal, 933, 104, 10.3847/1538-4357/ac74b5

    2022 doi

  37. [47]

    C., Karagiannis, D., et al

    Libanore, S., Artale, M. C., Karagiannis, D., et al. 2021, Journal of Cosmology and Astroparticle Physics, 2021, 035, 10.1088/1475-7516/2021/02/035

    2021 doi

  38. [48]

    2015, Astronomy and Computing, 13, 12, 10.1016/j.ascom.2015.09.003

    Nelson, D., Pillepich, A., Genel, S., et al. 2015, Astronomy and Computing, 13, 12, 10.1016/j.ascom.2015.09.003

    2015 doi

  39. [49]

    D., Bird, S., et al

    Ni, Y., Matteo, T. D., Bird, S., et al. 2022, Monthly Notices of the Royal Astronomical Society, 513, 670, 10.1093/mnras/stac351

    2022 doi

  40. [50]

    P., & Steinhardt, P

    Ostriker, J. P., & Steinhardt, P. J. 1995, Nature, 377, 600, 10.1038/377600a0

    1995 doi

  41. [51]

    D., & Thrane, E

    Payne, E., Banagiri, S., Lasky, P. D., & Thrane, E. 2020, Physical Review D, 102, 102004, 10.1103/PhysRevD.102.102004

    2020 doi

  42. [52]

    Peron, M., Ravenni, A., Libanore, S., Liguori, M., & Artale, M. C. 2024, Monthly Notices of the Royal Astronomical Society, 530, 1129, 10.1093/mnras/stae893

    2024 doi

  43. [53]

    2019, Monthly Notices of the Royal Astronomical Society, 490, 3196, 10.1093/mnras/stz2338

    Pillepich, A., Nelson, D., Springel, V., et al. 2019, Monthly Notices of the Royal Astronomical Society, 490, 3196, 10.1093/mnras/stz2338

    2019 doi

  44. [54]

    2016, Monthly Notices of the Royal Astronomical Society, 458, 2371, 10.1093/mnras/stw456

    Rodriguez-Gomez, V., Genel, S., Vogelsberger, M., et al. 2016, Monthly Notices of the Royal Astronomical Society, 458, 2371, 10.1093/mnras/stw456

    2016 doi

  45. [55]

    2020, Exploring galaxies-gravitational waves cross-correlations as an astrophysical probe, 10.48550/arXiv.2007.08534

    Scelfo, G., Boco, L., Lapi, A., & Viel, M. 2020, Exploring galaxies-gravitational waves cross-correlations as an astrophysical probe, 10.48550/arXiv.2007.08534

    2020 doi arXiv

  46. [56]

    2019, Phys

    Schmittfull, M., Simonovi c \' c , M., Assassi, V., & Zaldarriaga, M. 2019, Phys. Rev. D, 100, 043514, 10.1103/PhysRevD.100.043514

    2019 doi

  47. [57]

    2022, Research in Astronomy and Astrophysics, 22, 015006, 10.1088/1674-4527/ac32b4

    Shao, X., Cao, Z., Fan, X., & Wu, S. 2022, Research in Astronomy and Astrophysics, 22, 015006, 10.1088/1674-4527/ac32b4

    2022 doi

  48. [58]

    2015, Monthly Notices of the Royal Astronomical Society, 452, 575, 10.1093/mnras/stv1340

    Sijacki, D., Vogelsberger, M., Genel, S., et al. 2015, Monthly Notices of the Royal Astronomical Society, 452, 575, 10.1093/mnras/stv1340

    2015 doi

  49. [59]

    Singh, J., Monaco, P., & Tan, J. C. 2023, Mon. Not. R. Astron. Soc., 525, 969, 10.1093/mnras/stad2346

    2023 doi

  50. [60]

    2019, Corrfunc Project

    Sinha, M. 2019, Corrfunc Project

    2019

  51. [61]

    2019, Monthly Notices of the Royal Astronomical Society, 491, 3022, 10.1093/mnras/stz3157

    Sinha, M., & Garrison, L. 2019, Monthly Notices of the Royal Astronomical Society, 491, 3022, 10.1093/mnras/stz3157

    2019 doi

  52. [62]

    2025, American Astronomical Society Meeting Abstracts, 245, 349.06

    Smith, W., Jani, K., Holley-Bockelmann, K., & Mapelli, M. 2025, American Astronomical Society Meeting Abstracts, 245, 349.06. https://ui.adsabs.harvard.edu/abs/2025AAS...24534906S

    2025

  53. [63]

    Springel, V., White, S. D. M., Tormen, G., & Kauffmann, G. 2001, Monthly Notices of the Royal Astronomical Society, 328, 726, 10.1046/j.1365-8711.2001.04912.x

    2001

  54. [64]

    2018, Monthly Notices of the Royal Astronomical Society, 475, 676, 10.1093/mnras/stx3304

    Springel, V., Pakmor, R., Pillepich, A., et al. 2018, Monthly Notices of the Royal Astronomical Society, 475, 676, 10.1093/mnras/stx3304

    2018 doi

  55. [65]

    2021, Monthly Notices of the Royal Astronomical Society, 501, 970, 10.1093/mnras/staa3613

    Stiskalek, R., Veitch, J., & Messenger, C. 2021, Monthly Notices of the Royal Astronomical Society, 501, 970, 10.1093/mnras/staa3613

    2021 doi

  56. [66]

    G., Scoccimarro, R., Crocce, M., et al

    Sánchez, A. G., Scoccimarro, R., Crocce, M., et al. 2017, Monthly Notices of the Royal Astronomical Society, 464, 1640, 10.1093/mnras/stw2443

    2017 doi

  57. [67]

    2021, Mon

    To, C.-H., Krause, E., Rozo, E., et al. 2021, Mon. Not. R. Astron. Soc., 502, 4093, 10.1093/mnras/stab239

    2021 doi

  58. [68]

    Van Son, L. A. C., de Mink, S. E., Callister, T., et al. 2022, arXiv e-prints. 2110.01634

    2022 arXiv

  59. [69]

    Vijaykumar, A., Saketh, M. V. S., Kumar, S., Ajith, P., & Roy Choudhury, T. 2023, Physical Review D, 108, 103017, 10.1103/PhysRevD.108.103017

    2023 doi

  60. [70]

    2014, Nature, 509, 177, 10.1038/nature13316

    Vogelsberger, M., Genel, S., Springel, V., et al. 2014, Nature, 509, 177, 10.1038/nature13316

    2014 doi

  61. [71]

    J., & Dolence, J

    Wang, Y., Brunner, R. J., & Dolence, J. C. 2013, Monthly Notices of the Royal Astronomical Society, 432, 1961, 10.1093/mnras/stt450

    2013 doi

  62. [72]

    2019, Monthly Notices of the Royal Astronomical Society, 483, 503, 10.1093/mnras/sty3126

    Yang, Q., Hu, B., & Li, X.-D. 2019, Monthly Notices of the Royal Astronomical Society, 483, 503, 10.1093/mnras/sty3126

    2019 doi

  63. [73]

    J., van den Bosch, F

    Yang, X., Mo, H. J., van den Bosch, F. C., & Jing, Y. P. 2005, Monthly Notices of the Royal Astronomical Society, 357, 608, 10.1111/j.1365-2966.2005.08667.x

    2005

  64. [74]

    2023, Monthly Notices of the Royal Astronomical Society, 522, 3935, 10.1093/mnras/stad1275

    Yuan, S., Zamora, A., & Abel, T. 2023, Monthly Notices of the Royal Astronomical Society, 522, 3935, 10.1093/mnras/stad1275

    2023 doi

  65. [75]

    H., Wang, Y., et al

    Yuan, S., Wechsler, R. H., Wang, Y., et al. 2025, Mon. Not. R. Astron. Soc., 538, 1216, 10.1093/mnras/staf368

    2025 doi

  66. [76]

    2024, Monthly Notices of the Royal Astronomical Society, Advance Access, 10.1093/mnras/stae2513

    Yue, S., Feng, L., Ju, W., et al. 2024, Monthly Notices of the Royal Astronomical Society, Advance Access, 10.1093/mnras/stae2513

    2024 doi

  67. [77]

    H., et al

    Zehavi, I., Zheng, Z., Weinberg, D. H., et al. 2011, The Astrophysical Journal, 736, 10.1088/0004-637x/736/1/59

    2011 doi

  68. [78]

    2023, The Astrophysical Journal, 961

    Zhang, Y., Wang, W., Han, J., et al. 2023, The Astrophysical Journal, 961. https://api.semanticscholar.org/CorpusID:264490960

    2023

  69. [79]

    2023, Astronomy & Astrophysics, 672, A83, 10.1051/0004-6361/202346015

    Zhao, C. 2023, Astronomy & Astrophysics, 672, A83, 10.1051/0004-6361/202346015

    2023 doi

Pith tools

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