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REVIEW 2 major objections 6 minor 53 references

At fixed mass, dark-matter haloes in underdense regions show 1.5–1.8 times stronger intrinsic alignments than those in overdense regions.

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 →

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2026-07-14 06:57 UTC pith:2DIEG6ST

load-bearing objection Clean mass-matched measurement showing underdense haloes have ~1.5–1.8 imes larger A_IA; solid simulation result with residual assembly-bias caveats that do not reverse the signal. the 2 major comments →

arxiv 2607.11114 v1 pith:2DIEG6ST submitted 2026-07-13 astro-ph.CO

The Environmental Dependence of Halo Intrinsic Alignments: Stronger Signals in Underdense Regions

Masaya Ichikawa , Jingjing Shi , Toshiki Kurita , Masahiro Takada , Takahiro Nishimichi , Linda Blot This is my paper
classification astro-ph.CO
keywords intrinsic alignmentsweak gravitational lensingdark matter haloeslarge-scale environmentassembly biasN-body simulationscosmic shear systematics
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.

Intrinsic alignment (IA) is the tendency of galaxies and the dark-matter haloes that host them to point along the large-scale cosmic tidal field. It is a major contaminant for weak-lensing cosmology and is usually modelled as depending mainly on mass and redshift. This paper shows that the large-scale environment matters as well. Using high-resolution N-body simulations, the authors rank every halo by the overdensity of neighbours inside an 8 h^{-1} Mpc sphere, then compare the densest and sparsest 30 % of haloes inside narrow mass bins so that the two samples have identical mass distributions. The underdense sample has an IA amplitude 1.5–1.8 times larger than the overdense sample of the same mass, across all masses and redshifts they probe (z = 0.1–1.5). The contrast grows toward low redshift. An orientation-only estimator reveals that underdense haloes are both more elongated and more faithfully aligned with the large-scale tide. The result implies that any sample whose galaxies preferentially sit in voids or clusters will carry a systematically different IA amplitude even at fixed mass, and that environment-sensitive weak-lensing statistics will be especially affected.

Core claim

At fixed halo mass, dark-matter haloes that live in underdense large-scale environments have systematically larger intrinsic-alignment amplitudes A_IA than those that live in overdense environments, by a factor of roughly 1.5–1.8. The contrast holds across the mass and redshift range 10^{12}–10^{14} h^{-1} M_⊙ and z = 0.1–1.5 and is produced by two reinforcing effects: underdense haloes are intrinsically less spherical and their orientations track the large-scale tidal field more strongly.

What carries the argument

Mass-matched environmental ranking by δ_8 (neighbour-count overdensity inside 8 h^{-1} Mpc) combined with the linear-alignment fit of the monopole P_δE, plus a unit-ellipticity orientation-only estimator that separates shape magnitude from pure orientation alignment.

Load-bearing premise

That cutting the upper and lower 30 % of δ_8 inside mass bins fully removes mass (and any secondary assembly properties correlated with mass) so that residual differences in alignment can be attributed only to environment.

What would settle it

Repeat the same mass-matched δ_8 split on an independent high-resolution simulation or on a spectroscopic galaxy sample that can measure both large-scale density and projected shapes; if the underdense-to-overdense A_IA ratio collapses to unity once mass and concentration are controlled, the claimed environmental signal is absent.

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

If this is right

  • IA models used in weak-lensing analyses that depend only on mass (or luminosity) and redshift will mis-estimate the contamination whenever a sample is environmentally biased.
  • Beyond-two-point probes that deliberately split by density, voids or cosmic web will inherit an environment-dependent IA term larger than standard two-point forecasts assume.
  • Underdense regions may retain a cleaner record of the primordial tidal field, so IA spectra measured there can supply cosmological information complementary to the density power spectrum.
  • The observed anti-correlation of A_IA with halo bias at fixed mass constitutes an ‘alignment assembly bias’ that any secondary-bias model of halo shapes must reproduce.

Where Pith is reading between the lines

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

  • Surveys that select luminous red galaxies in clusters versus field ellipticals of the same stellar mass should already show a measurable difference in IA amplitude of order 50 %.
  • Density-split lensing and void-lensing pipelines will need an environment-dependent IA nuisance parameter; omitting it will bias the inferred growth rate or S_8 at a level comparable to current statistical errors.
  • If the memory of the large-scale tide is erased mainly by mergers, then formation-time or concentration splits at fixed mass should recover a similar alignment contrast, offering a cheap observational cross-check.

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. The paper measures the environmental dependence of dark-matter halo intrinsic alignments in the Dark Quest N-body suite over z=0.1–1.5. Environment is quantified by the neighbour overdensity δ8 within 8 h^{-1} Mpc; overdense and underdense subsamples are defined as the upper/lower 30% of δ8 within 20 logarithmic mass bins so that the two samples share the same mass distribution. Using the linear-alignment model as a fitting template on large scales (0.02 < k < 0.07 h Mpc^{-1}), the authors report that underdense haloes have systematically larger IA amplitudes A_IA than mass-matched overdense haloes, by a factor ∼1.5–1.8, with the contrast strengthening toward low redshift. An orientation-only (unit-ellipticity) estimator, together with rms ellipticity and 3-D axis-ratio measurements, is used to show that the contrast arises from both stronger orientation alignment and greater intrinsic elongation of underdense haloes. Appendices address non-Poisson noise in P_EE, alternative inertia-tensor definitions, three-dimensional shapes, and the relation of A_IA to halo bias.

Significance. If the mass-matched environmental contrast holds, the result is a clear, quantitative demonstration that large-scale environment is a secondary driver of halo IA at fixed mass—an “alignment assembly bias” with direct implications for modelling IA in weak-lensing cosmology, especially for beyond-two-point and environment-selected analyses (density-split, voids, field-level inference). Strengths of the work include a carefully designed mass-matching procedure, restriction of A_IA fits to the linear regime, cross-checks with an orientation-only estimator and an alternative inertia tensor (Appendix B), B-mode-based noise assessment (Appendix A), and three-dimensional shape measurements (Appendix C). The measurement is falsifiable and reproducible from the stated catalogues and estimators; the paper does not claim a parameter-free derivation, but a controlled simulation measurement, which is the appropriate standard here.

major comments (2)
  1. [§2.2, Fig. 2, §4] §2.2 and Fig. 2: the mass-binned 30-percentile cut on δ8 removes the mass–environment degeneracy by construction, but does not control secondary assembly variables (concentration, formation time, spin) that are known to correlate with both environment and shape response (cf. Akitsu et al. 2021, cited). The residual A_IA contrast is therefore rigorously “at fixed mass and δ8 rank,” not necessarily pure environment independent of assembly history. The central numerical claim is not overturned, but §4’s framing as environmental dependence should state this residual degeneracy explicitly, and a brief check (e.g., mean concentration or formation redshift of the two subsamples, or a partial re-match) would substantially strengthen the interpretation.
  2. [§3.1, Table 1, Fig. 4, Appendix A] §3.1 and Table 1: A_IA is fitted exclusively from the monopole of P_δE over 0.02 < k < 0.07 h Mpc^{-1}, which is appropriate and more robust to density weighting than P_EE. However, the text still leans on P_EE (Fig. 4) for qualitative support, where non-Poisson noise and the (1+δ_h)^{2} boost are large for the overdense, high-bias sample (Appendix A; b_h ≃ 6 for the massive z=1.5 bin). The paper should state more clearly that the quantitative underdense-to-overdense ratios in Table 1 and Fig. 5 rest on P_δE alone, and that P_EE is used only as a consistency check after B-mode subtraction, so that the reader does not over-weight the noisier auto-spectrum panels.
minor comments (6)
  1. [Fig. 5, §2.2] Fig. 5: the intermediate (middledense) points are mentioned in the caption and Appendix D but the construction of the intermediate subsample (e.g., middle 40%?) is not stated in §2.2; a one-sentence definition would help.
  2. [§2.4.2, §3.1] Eqs. (2.15)–(2.16) and the fit model in §3.1: the text writes P_δE^{(0)} = (2/3) b_K P_δδ with b_K = C1 ρ_cr Ω_m A_IA / D(z). A short note that the 2/3 factor is the μ-average of (1−μ^{2}) would make the monopole conversion fully explicit.
  3. [Table 1] Table 1: the column headers mix A_IA, Â_IA, e_rms, and b_h; a brief table note defining the orientation-only estimator and the k-range used for b_h would improve readability without hunting through the text.
  4. [§4] §4 discussion of Xia et al. [28] and Herle et al. [53]: the reconciliation via density weighting and web-vs-δ8 classification is useful; a single sentence noting that a like-for-like δ8 comparison in those samples is left for future work would avoid overstating the resolution of the tension.
  5. [Author list, Data Availability] Minor typographical issues: “T oshiki” and “T akada” in the author list (space after T); “A vailability” in Data Availability; and occasional missing spaces around δ8 subscripts in the abstract/intro. These are cosmetic.
  6. [Appendix C, Fig. 11] Appendix C, Fig. 11 (right): the non-monotonic mass trend of c/a at low z is interesting but not used in the main argument; either a one-line link to the IA mass trend or a shorter caption would keep the appendix focused.

Circularity Check

0 steps flagged

No significant circularity: direct N-body measurement of mass-matched IA spectra; A_IA is a fitted amplitude, not a derived prediction forced by inputs.

full rationale

The paper measures P_δE and P_EE from Dark Quest halo catalogues, constructs mass-matched overdense/underdense subsamples via a δ_8 percentile cut within mass bins (§2.2), and reports the ratio of best-fit linear-alignment amplitudes A_IA over a fixed k-window. The LA/NLA template (Eqs. 2.14–2.16) is taken from the external literature (Hirata & Seljak 2004; Bridle & King 2007) and used only as a fitting function; the fitted A_IA values and their underdense/overdense ratios are the results themselves, not predictions of a closely related observable. Orientation-only and alternative-inertia-tensor estimators, 3-D axis ratios, and B-mode noise subtraction are independent cross-checks, not re-statements of the fit. Self-citations (Nishimichi et al. for the simulation suite; Kurita et al. for the inertia-tensor and power-spectrum pipeline) supply data and methods; they do not supply a uniqueness theorem or ansatz that forces the environmental contrast. Residual assembly-bias matching is an interpretive caveat already noted by the authors, not a circular reduction of the measured signal. Score 1 reflects only the ordinary methodological self-citation, which is not load-bearing for the central claim.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central claim is an empirical measurement from N-body simulations. It rests on standard cosmological assumptions, a conventional environment proxy, a conventional shape estimator, and a linear-alignment fitting template whose overall normalisation is free. No new physical entities are postulated; free parameters are the fitted A_IA values and analysis choices (percentile cut, k-range, smoothing scale).

free parameters (4)
  • A_IA (per subsample) = ~9.9–28 depending on mass, z, environment (Table 1)
    Dimensionless amplitude fitted by χ² minimisation of P_δE^(0) to the measured matter power spectrum over 0.02 < k < 0.07 h Mpc^{-1}; the environmental ratio is built from these fitted values.
  • C1 ρ_cr0 = 0.0134
    Overall normalisation of the linear-alignment model fixed to the conventional value 0.0134; absorbed into the definition of A_IA.
  • δ8 percentile cut (30 %) = upper/lower 30 %
    Arbitrary threshold used to define overdense/underdense subsamples inside each mass bin; changes the sample size and extreme-environment contrast.
  • fitting k-range = 0.02 < k < 0.07 h Mpc^{-1}
    Chosen by hand (0.02–0.07 h Mpc^{-1}) to stay inside the linear regime while avoiding sample-variance-dominated large scales.
axioms (5)
  • domain assumption Linear (non-linear) alignment model: halo shapes respond linearly to the large-scale tidal field on the fitted scales.
    Used as the fitting template in §2.4.2 and §3; validity assumed for k ≲ 0.1 h Mpc^{-1}.
  • domain assumption δ8 measured from neighbouring haloes within 8 h^{-1} Mpc is a faithful tracer of the quasi-linear large-scale environment.
    Definition in §2.2; motivated by prior clustering literature but not uniquely privileged.
  • ad hoc to paper Mass-matching within 20 logarithmic bins removes the mass–environment degeneracy sufficiently that residual A_IA differences are environmental.
    Core methodological claim of §2.2; secondary assembly variables remain unmatched.
  • domain assumption Reduced iterative inertia tensor yields shapes whose large-scale IA spectra differ from other definitions only by a constant factor.
    Justified by reference to Kurita et al. Appendix C and re-checked in this paper’s Appendix B.
  • domain assumption B-mode power on large scales is pure shape noise (no IA signal).
    Used in Appendix A to subtract non-Poisson noise from P_EE.

pith-pipeline@v1.1.0-grok45 · 22666 in / 3526 out tokens · 35341 ms · 2026-07-14T06:57:45.110387+00:00 · methodology

0 comments
read the original abstract

The intrinsic alignment (IA) of galaxies and the dark matter haloes that host them is one of the leading astrophysical systematics for weak-lensing cosmology, yet how the IA signal depends on the large-scale environment in which haloes reside is not yet fully characterised. We use the high-resolution $N$-body simulations of the Dark Quest suite to measure the environmental dependence of the IA of dark matter haloes over the redshift range $z=0.1$--$1.5$. We quantify each halo's environment through the overdensity $\delta_8$, defined from the number of neighbouring haloes within $8\, h^{-1}Mpc$, and we isolate the environmental effect from its degeneracy with the halo-mass dependence by comparing the most overdense and most underdense haloes constructed to share the same halo-mass distribution. We find that haloes in underdense environments exhibit systematically larger IA amplitudes $A_{\rm IA}$ than haloes of the same mass in overdense environments, by a factor of $\sim1.5$--$1.8$, and that this trend persists across the mass and redshift ranges probed, strengthening towards low redshift. Using an orientation-only (unit-ellipticity) estimator, we further show that this environmental contrast is driven by a combination of two effects: haloes in underdense regions are both intrinsically less spherical and more strongly aligned with the large-scale tidal field than their overdense counterparts of the same mass. These results indicate that the large-scale environment is a non-negligible variable in modelling halo and galaxy alignments, and may be a particularly important factor for beyond-two-point weak-lensing analyses.

discussion (0)

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Reference graph

Works this paper leans on

53 extracted references · 40 linked inside Pith

  1. [1]

    Bartelmann and P

    M. Bartelmann and P. Schneider,Weak gravitational lensing,Phys. Rep.340(2001) 291 [astro-ph/9912508]

    Pith/arXiv arXiv 2001

  2. [2]

    Hoekstra and B

    H. Hoekstra and B. Jain,Weak Gravitational Lensing and its Cosmological Applications, Annual Review of Nuclear and Particle Science58(2008) 99 [0805.0139]

    Pith/arXiv arXiv 2008

  3. [3]

    Kilbinger,Cosmology with cosmic shear observations: a review,Reports on Progress in Physics78(2015) 086901 [1411.0115]

    M. Kilbinger,Cosmology with cosmic shear observations: a review,Reports on Progress in Physics78(2015) 086901 [1411.0115]

    Pith/arXiv arXiv 2015

  4. [4]

    Hirata and U.c.v

    C.M. Hirata and U.c.v. Seljak,Intrinsic alignment-lensing interference as a contaminant of cosmic shear,Phys. Rev. D70(2004) 063526

    2004

  5. [5]

    Bridle and L

    S. Bridle and L. King,Dark energy constraints from cosmic shear power spectra: impact of intrinsic alignments on photometric redshift requirements,New Journal of Physics9(2007) 444 [0705.0166]

    Pith/arXiv arXiv 2007

  6. [6]

    Troxel and M

    M.A. Troxel and M. Ishak,The intrinsic alignment of galaxies and its impact on weak gravitational lensing in an era of precision cosmology,Phys. Rep.558(2015) 1 [1407.6990]

    Pith/arXiv arXiv 2015

  7. [7]

    Joachimi, M

    B. Joachimi, M. Cacciato, T.D. Kitching, A. Leonard, R. Mandelbaum, B.M. Schäfer et al., Galaxy Alignments: An Overview,Space Sci. Rev.193(2015) 1 [1504.05456]

    Pith/arXiv arXiv 2015

  8. [8]

    Lamman, E

    C. Lamman, E. Tsaprazi, J. Shi, N.N. Šarčević, S. Pyne, E. Legnani et al.,The IA Guide: A Breakdown of Intrinsic Alignment Formalisms,The Open Journal of Astrophysics7(2024) [2309.08605]

    Pith/arXiv arXiv 2024

  9. [9]

    Chisari,A rising tide: intrinsic alignments since the turn of the millennium,A&A Rev

    N.E. Chisari,A rising tide: intrinsic alignments since the turn of the millennium,A&A Rev. 33(2025) 5 [2510.15738]

    arXiv 2025

  10. [10]

    Krause, T

    E. Krause, T. Eifler and J. Blazek,The impact of intrinsic alignment on current and future cosmic shear surveys,MNRAS456(2016) 207 [1506.08730]

    Pith/arXiv arXiv 2016

  11. [11]

    Catelan, M

    P. Catelan, M. Kamionkowski and R.D. Blandford,Intrinsic and extrinsic galaxy alignment, Monthly Notices of the Royal Astronomical Society320(2001) L7–L13

    2001

  12. [12]

    Blazek, N

    J.A. Blazek, N. MacCrann, M.A. Troxel and X. Fang,Beyond linear galaxy alignments, Phys. Rev. D100(2019) 103506 [1708.09247]

    Pith/arXiv arXiv 2019

  13. [13]

    Vlah, N.E

    Z. Vlah, N.E. Chisari and F. Schmidt,An EFT description of galaxy intrinsic alignments, JCAP2020(2020) 025 [1910.08085]. – 15 –

    Pith/arXiv arXiv 2020

  14. [14]

    Vlah, N.E

    Z. Vlah, N.E. Chisari and F. Schmidt,Galaxy shape statistics in the effective field theory, Journal of Cosmology and Astroparticle Physics2021(2021) 061

    2021

  15. [15]

    T. Bakx, T. Kurita, N. Elisa Chisari, Z. Vlah and F. Schmidt,Effective field theory of intrinsic alignments at one loop order: a comparison to dark matter simulations,JCAP2023(2023) 005 [2303.15565]

    Pith/arXiv arXiv 2023

  16. [16]

    Chen and N

    S.-F. Chen and N. Kokron,A Lagrangian theory for galaxy shape statistics,JCAP2024(2024) 027 [2309.16761]

    Pith/arXiv arXiv 2024

  17. [17]

    Singh, R

    S. Singh, R. Mandelbaum and S. More,Intrinsic alignments of SDSS-III BOSS LOWZ sample galaxies,MNRAS450(2015) 2195 [1411.1755]

    Pith/arXiv arXiv 2015

  18. [18]

    Johnston, C

    H. Johnston, C. Georgiou, B. Joachimi, H. Hoekstra, N.E. Chisari, D. Farrow et al., KiDS+GAMA: Intrinsic alignment model constraints for current and future weak lensing cosmology,A&A624(2019) A30 [1811.09598]

    Pith/arXiv arXiv 2019

  19. [19]

    Siegel, J

    J. Siegel, J. McCullough, A. Amon, C. Lamman, N. Jeffrey, B. Joachimi et al.,Intrinsic alignment demographics for next-generation lensing: Revealing galaxy property trends with DESI Y1 direct measurements,arXiv e-prints(2025) arXiv:2507.11530 [2507.11530]

    Pith/arXiv arXiv 2025

  20. [20]

    Vlah, N.E

    Z. Vlah, N.E. Chisari and F. Schmidt,Galaxy shape statistics in the effective field theory, JCAP2021(2021) 061 [2012.04114]

    Pith/arXiv arXiv 2021

  21. [21]

    Kurita and M

    T. Kurita and M. Takada,Analysis method for 3D power spectrum of projected tensor fields with fast estimator and window convolution modeling: An application to intrinsic alignments, Phys. Rev. D105(2022) 123501 [2202.11839]

    Pith/arXiv arXiv 2022

  22. [22]

    Akitsu, Y

    K. Akitsu, Y. Li and T. Okumura,Quadratic shape biases in three-dimensional halo intrinsic alignments,JCAP2023(2023) 068 [2306.00969]

    Pith/arXiv arXiv 2023

  23. [23]

    Akitsu, T

    K. Akitsu, T. Kurita, T. Nishimichi, M. Takada and S. Tanaka,Imprint of anisotropic primordial non-Gaussianity on halo intrinsic alignments in simulations,Phys. Rev. D103 (2021) 083508 [2007.03670]

    Pith/arXiv arXiv 2021

  24. [24]

    Kurita and M

    T. Kurita and M. Takada,Constraints on anisotropic primordial non-Gaussianity from intrinsic alignments of SDSS-III BOSS galaxies,Phys. Rev. D108(2023) 083533 [2302.02925]

    Pith/arXiv arXiv 2023

  25. [25]

    Okumura and A

    T. Okumura and A. Taruya,First Constraints on Growth Rate from Redshift-space Ellipticity Correlations of SDSS Galaxies at 0.16 < z < 0.70,ApJL945(2023) L30 [2301.06273]

    Pith/arXiv arXiv 2023

  26. [26]

    Kurita, D

    T. Kurita, D. Jamieson, E. Komatsu and F. Schmidt,Parity violation in galaxy shapes: Primordial non-Gaussianity,Phys. Rev. D113(2026) 063557 [2509.08787]

    Pith/arXiv arXiv 2026

  27. [27]

    J. Shi, H. Wang and H.J. Mo,Flow Patterns around Dark Matter Halos: The Link between Halo Dynamical Properties and Large-scale Tidal Field,ApJ807(2015) 37 [1501.07764]

    Pith/arXiv arXiv 2015

  28. [28]

    Q. Xia, X. Kang, P. Wang, Y. Luo, X. Yang, Y. Jing et al.,Halo Intrinsic Alignment: Dependence on Mass, Formation Time, and Environment,ApJ848(2017) 22 [1710.01730]

    Pith/arXiv arXiv 2017

  29. [29]

    Akitsu, Y

    K. Akitsu, Y. Li and T. Okumura,Cosmological simulation in tides: power spectra, halo shape responses, and shape assembly bias,JCAP2021(2021) 041 [2011.06584]

    Pith/arXiv arXiv 2021

  30. [30]

    Reischke and B.M

    R. Reischke and B.M. Schäfer,Environmental dependence of ellipticity correlation functions of intrinsic alignments,JCAP2019(2019) 031 [1812.06918]

    Pith/arXiv arXiv 2019

  31. [31]

    d’Assignies D., N.E

    W. d’Assignies D., N.E. Chisari, N. Hamaus and S. Singh,Intrinsic alignments of galaxies around cosmic voids,MNRAS509(2022) 1985 [2108.03922]

    Pith/arXiv arXiv 2022

  32. [32]

    Nishimichi, M

    T. Nishimichi, M. Takada, R. Takahashi, K. Osato, M. Shirasaki, T. Oogi et al.,Dark quest. i. fast and accurate emulation of halo clustering statistics and its application to galaxy clustering, The Astrophysical Journal884(2019) 29

    2019

  33. [33]

    Planck Collaboration, Ade, P. A. R., Aghanim, N., Arnaud, M., Ashdown, M., Aumont, J. et al.,Planck 2015 results - xiii. cosmological parameters,A&A594(2016) A13. – 16 –

    2015

  34. [34]

    Lewis, A

    A. Lewis, A. Challinor and A. Lasenby,Efficient computation of cosmic microwave background anisotropies in closed friedmann-robertson-walker models,The Astrophysical Journal538 (2000) 473

    2000

  35. [35]

    R. Scoccimarro,Transients from initial conditions: a perturbative analysis,Monthly Notices of the Royal Astronomical Society299(1998) 1097 [https://academic.oup.com/mnras/article-pdf/299/4/1097/3869550/299-4-1097.pdf]

    1998

  36. [36]

    Crocce, S

    M. Crocce, S. Pueblas and R. Scoccimarro,Transients from initial conditions in cosmological simulations,Monthly Notices of the Royal Astronomical Society373(2006) 369 [https://academic.oup.com/mnras/article-pdf/373/1/369/4187617/mnras0373-0369.pdf]

    2006

  37. [37]

    V. Springel,The cosmological simulation code gadget-2,Monthly Notices of the Royal Astronomical Society364(2005) 1105 [https://academic.oup.com/mnras/article-pdf/364/4/1105/18657201/364-4-1105.pdf]

    2005

  38. [38]

    Behroozi, R.H

    P.S. Behroozi, R.H. Wechsler and H.-Y. Wu,The rockstar phase-space temporal halo finder and the velocity offsets of cluster cores,The Astrophysical Journal762(2012) 109

    2012

  39. [39]

    Abbas and R.K

    U. Abbas and R.K. Sheth,Strong clustering of underdense regions and the environmental dependence of clustering from gaussian initial conditions,Monthly Notices of the Royal Astronomical Society378(2007) 641–648

    2007

  40. [40]

    Kurita, M

    T. Kurita, M. Takada, T. Nishimichi, R. Takahashi, K. Osato and Y. Kobayashi,Power spectrum of halo intrinsic alignments in simulations,Monthly Notices of the Royal Astronomical Society501(2020) 833–852

    2020

  41. [41]

    Osato, T

    K. Osato, T. Nishimichi, M. Oguri, M. Takada and T. Okumura,Strong orientation dependence of surface mass density profiles of dark haloes at large scales,MNRAS477(2018) 2141 [1712.00094]

    Pith/arXiv arXiv 2018

  42. [42]

    J. Shi, T. Kurita, M. Takada, K. Osato, Y. Kobayashi and T. Nishimichi,Power spectrum of intrinsic alignments of galaxies in illustristng,Journal of Cosmology and Astroparticle Physics 2021(2021) 030 [2009.00276]

    Pith/arXiv arXiv 2021

  43. [43]

    Bernstein and M

    G.M. Bernstein and M. Jarvis,Shapes and Shears, Stars and Smears: Optimal Measurements for Weak Lensing,AJ123(2002) 583 [astro-ph/0107431]

    Pith/arXiv arXiv 2002

  44. [44]

    Van Alfen, D

    N. Van Alfen, D. Campbell, J. Blazek, C.D. Leonard, F. Lanusse, A. Hearin et al.,An Empirical Model For Intrinsic Alignments: Insights From Cosmological Simulations,The Open Journal of Astrophysics7(2024) [2311.07374]

    Pith/arXiv arXiv 2024

  45. [45]

    Sheth and G

    R.K. Sheth and G. Tormen,On the environmental dependence of halo formation,MNRAS350 (2004) 1385 [astro-ph/0402237]

    Pith/arXiv arXiv 2004

  46. [46]

    L. Gao, V. Springel and S.D.M. White,The age dependence of halo clustering,MNRAS363 (2005) L66 [astro-ph/0506510]

    Pith/arXiv arXiv 2005

  47. [47]

    Gao and S.D.M

    L. Gao and S.D.M. White,Assembly bias in the clustering of dark matter haloes,MNRAS377 (2007) L5 [astro-ph/0611921]

    Pith/arXiv arXiv 2007

  48. [48]

    Y.P. Jing, Y. Suto and H.J. Mo,The Dependence of Dark Halo Clustering on Formation Epoch and Concentration Parameter,ApJ657(2007) 664 [astro-ph/0610099]

    Pith/arXiv arXiv 2007

  49. [49]

    Dalal, M

    N. Dalal, M. White, J.R. Bond and A. Shirokov,Halo Assembly Bias in Hierarchical Structure Formation,ApJ687(2008) 12 [0803.3453]

    Pith/arXiv arXiv 2008

  50. [50]

    Faltenbacher and S.D.M

    A. Faltenbacher and S.D.M. White,Assembly Bias and the Dynamical Structure of Dark Matter Halos,ApJ708(2010) 469 [0909.4302]

    Pith/arXiv arXiv 2010

  51. [51]

    Shi and R.K

    J. Shi and R.K. Sheth,Dependence of halo bias on mass and environment,MNRAS473(2018) 2486 [1707.04096]. – 17 –

    Pith/arXiv arXiv 2018

  52. [52]

    Okumura and Y.P

    T. Okumura and Y.P. Jing,The Gravitational Shear-Intrinsic Ellipticity Correlation Functions of Luminous Red Galaxies in Observation and in theΛCDM Model,ApJL694(2009) L83 [0812.2935]

    Pith/arXiv arXiv 2009

  53. [53]

    renormalised

    A. Herle, N.E. Chisari, H. Hoekstra and D. Neumann,Assembly bias and the redshift evolution of intrinsic alignments for LRGs,arXiv e-prints(2026) arXiv:2607.00785 [2607.00785]. A Non-Poisson noise inP EE The shape auto-power spectraP EE andP BB both contain a shape-noise contribution that arises from the finite number of haloes sampling the shape field [s...

    Pith/arXiv arXiv 2026