Pith. sign in

REVIEW 4 major objections 6 minor 46 references

Trinity VII. Predictions for the Observable Correlation Functions of Accreting Black Holes

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read The Trinity model, fit without any quasar clustering data, predicts the observed quasar correlation functions at 0<z<3.5 within error bars, implying that clustering adds little new information about where quasars live.

desk verdict Trinity's quasar clustering predictions are a useful validation, but the 'no correlation functions' claim is overstated and the comparison needs quantitative grounding. read the letter →

arxiv 2506.05612 v1 pith:J7PSRT7B submitted 2025-06-05 astro-ph.GA

Oddisey Knox , Haowen Zhang , Peter Behroozi This is my paper
classification astro-ph.GA
keywords quasarclusteringsupermassiveblackholeshalooccupationTrinitymodelAGNfractioncorrelationfunctionluminositydependencedarkmatterhalos
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

Trinity is an empirical model that infers how dark matter halos, galaxies, and supermassive black holes are linked, using constraints such as quasar luminosity functions, AGN occupation fractions, and the local SMBH–bulge mass relation, but never any quasar clustering data. This paper applies the best-fit Trinity model to a dark matter simulation and compares the predicted quasar autocorrelation functions with observations in $0

What carries the argument

The load-bearing object is the Trinity empirical model of the halo–galaxy–SMBH connection, which assigns each dark matter halo a probability $f_{>L_{\mathrm{thresh}}}(M_h,z)=\int_{L_{\mathrm{thresh}}}^{\infty} P(L|M_h,z)\,dL$ of hosting an actively accreting black hole above a given bolometric luminosity. Applied to the MDPL2 dark matter simulation, this weighting yields predicted projected and redshift-space correlation functions. The decisive feature is that Trinity was never fit to clustering measurements, so the agreement with observed $w_p$ and $\xi(s)$ is a pure, out-of-sample prediction of the model's placement of quasars within halos.

What would settle it

A measurement of quasar clustering for a well-characterized sample at $L_{\mathrm{bol}} \sim 10^{44}\,\mathrm{erg\,s^{-1}}$ at $z \sim 3$ with bias errors smaller than $\sim0.1$ dex would test the paper's luminosity-dependence claim: Trinity predicts that such a sample should cluster within $\sim0.3$ dex of the $L>10^{46}\,\mathrm{erg\,s^{-1}}$ population, so a larger deviation would falsify that prediction.

Watch

Extended reading notes

Core claim

The paper's central claim is that Trinity — a self-consistent empirical model of the halo–galaxy–SMBH connection that deliberately excluded quasar clustering from its fitting data — nonetheless reproduces the observed two-point projected and redshift-space quasar correlation functions across $0<z<3.5$ within the quoted uncertainties. Because the prediction was generated by the best-fit model with no correlation-function constraints, the agreement indicates that the halo-occupation information accessible through quasar clustering is largely redundant with information already present in AGN occupation fractions and luminosity functions. The paper further finds that predicted quasar clustering varies by less than $\sim0.3$ dex in bias between bolometric luminosity thresholds of $10^{42}$ and $10^{46}\,\mathrm{erg\,s^{-1}}$ at fixed redshift, since most SMBH growth occurs in halos of roughly $10^{12}$–$10^{13}\,M_\odot$. This shallow luminosity dependence explains the observed lack of luminosity dependence in quasar clustering.

Load-bearing premise

The comparison equates every observed optical quasar sample with a single bolometric luminosity cut at $L_{\mathrm{bol}} > 10^{46}\,\mathrm{erg\,s^{-1}}$, even though real surveys use magnitude and color cuts spanning a range of bolometric luminosities; if those selection differences correspond to different host halo mass distributions, the agreement could be coincidental.

Editorial extensions

If this is right

  • Because Trinity was not constrained by clustering data, agreement implies that quasar autocorrelation functions add no significant new information about SMBH halo occupation beyond AGN occupation fractions.
  • The predicted variation in clustering bias with luminosity stays below $\sim0.3$ dex from $10^{42}$ to $10^{46}\,\mathrm{erg\,s^{-1}}$, consistent with observations and identifying where the trend would need rare, bright quasars to be seen.
  • The model predicts the largest luminosity dependence on scales below $\sim5\,\mathrm{Mpc\,h^{-1}}$, but quasar number densities are too low for autocorrelations to exploit it; quasar–galaxy cross-correlations are the natural probe.
  • Because most luminous quasars occupy halos in a narrow mass range at every redshift tested, splitting samples by luminosity or black hole mass yields little clustering contrast — a restriction-of-range effect.

Reading between the lines

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

  • A sharper out-of-sample test would be to refit Trinity with quasar clustering included: the paper's logic predicts the posterior should barely move, so a large shift would expose hidden tension between clustering and occupation-fraction constraints.
  • The shallow luminosity dependence implies that current luminosity-binned samples would need roughly an order of magnitude more area to detect the predicted differences, a target that upcoming wide-area quasar surveys could plausibly meet.
  • The restriction-of-range argument suggests that grouping quasars by black hole virial mass will continue to show little clustering contrast, but the same argument implies that cross-correlating quasars with galaxies selected by stellar mass could reveal the underlying halo mass trend.
  • One testable extension is to compare Trinity's predicted quasar–galaxy cross-correlation functions against existing cross-correlation measurements, which the paper does not compute but which would validate the same halo-occupation placement at higher signal-to-noise.
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

4 major / 6 minor

Summary. The paper presents predictions of the projected and redshift-space two-point correlation functions of quasars from the Trinity empirical model, applied to the MDPL2 N-body simulation. Trinity's best-fit halo-galaxy-SMBH connection, which the authors state was not constrained by quasar clustering data, is used with a single bolometric luminosity threshold (L > 10^46 erg/s) to weight halos by the predicted fraction of time they host AGN above the threshold. The predicted wp(rp) and xi(s) are compared visually with a compilation of observed quasar clustering measurements from 2QZ, 2SLAQ, 2QDESp, SDSS, BOSS, and eBOSS over 0 < z < 3.5. The authors claim agreement within observational error bars and conclude that quasar clustering does not add significant information beyond AGN occupation fractions. They also predict a shallow luminosity dependence of quasar clustering and recommend quasar-galaxy cross-correlations as a more promising probe.

Significance. If the agreement is robust, the paper would provide an important demonstration that the halo-galaxy-SMBH connection inferred from luminosity functions and occupation fractions is consistent with quasar clustering, an independent test of Trinity. The luminosity-dependent predictions are falsifiable and useful, and the recommendation for cross-correlations is well reasoned. The paper also compiles a valuable set of observations. However, the lack of a quantitative comparison statistic and the a priori mapping of observed samples to a single luminosity threshold currently prevent the central claim from being fully supported.

major comments (4)
  1. [Section 2.3 and Abstract] Section 2.3 states that the galaxy-halo connection P(M*|Mh,z) is constrained by 'galaxy number densities and correlation functions,' while the Abstract and Section 1 say Trinity used 'constraints other than correlation functions' and 'no correlation function data.' These statements are contradictory. The paper's main claim that quasar clustering provides no additional information requires only that no quasar clustering data were used; please revise the Abstract and Introduction to say 'no quasar clustering constraints' and clarify in Section 2.3 that galaxy correlation functions do enter the model. Otherwise the reader cannot judge whether the prediction is truly independent of clustering data.
  2. [Section 3 and Section 5] Section 3 adopts L_thresh = 10^46 erg/s for all observed samples, citing 'typical luminosities' from Ross et al. (2009), but Table 1 includes surveys with very different depths (e.g., BOSS reaches two magnitudes deeper; 2SLAQ reaches g=21.85), and Appendix A shows the same samples contain quasars with L_bol = 10^45 - 10^46 erg/s. The model itself predicts some luminosity dependence (Fig. 5, especially at high L and small scales). If the effective luminosity distribution of an observed sample is centered below 10^46 erg/s, the predicted wp and xi(s) could differ from the single-threshold curve by more than the error bars, making the agreement coincidental. The acknowledgement in Section 5 that 'we cannot reproduce exactly' the selection criteria is not sufficient; please forward-model the bolometric luminosity distributions of each survey or demonstrate that the predictions are insensitive to a plausible range of effective L_thresh.
  3. [Section 4, Figures 1-4] The central claim that Trinity 'accurately predicts quasar correlation functions within observed error bars' is supported only by visual inspection. No goodness-of-fit statistic is reported, and the model is shown as a single curve with no uncertainty from the Trinity posterior or from the simulation box. This makes it impossible to judge whether deviations (e.g., the apparent downturn in xi(s) at ~2-5 Mpc for z < 2) are statistically significant. Please add a quantitative measure of agreement (e.g., chi-square with degrees of freedom, or a comparison of the inferred bias) and, if feasible, error bands on the model predictions.
  4. [Section 4, redshift-space xi(s)] The unscattered prediction appears to underpredict xi(s) at small separations in several redshift bins (e.g., z = 2.0-3.0 at ~2-3 Mpc). The paper introduces a 'tested' random scatter of 700 km/s, but this value is not derived from the model or the data; it is an additional parameter. If the agreement with xi(s) relies on this scatter, the claim that the model predicts the redshift-space clustering within error bars is not established for the unscattered model. Please either (a) show that the unscattered prediction is consistent within the quoted errors, or (b) treat the scatter as a systematic and state explicitly how the conclusions change without it.
minor comments (6)
  1. [Figure 10 caption] The caption for Figure 10 reads 'This is an example figure. Captions appear below each figure,' which is clearly placeholder text; a real caption must be provided, and the cross-reference 'Fig. 9 and ??' in Appendix A should be fixed.
  2. [Figures 1-4 and Table 1] The survey name is typeset inconsistently as 'da ˆAngela' in several captions and in Table 1; use 'da Ângela' consistently throughout.
  3. [Section 4] The phrases 'z≲2.0 at ≲5 Mpc' and 'z=2.0-3.0 from ~2-3 Mpc' are ambiguous; please specify the exact redshift bins and scale ranges intended.
  4. [Abstract] The abstract reports a change in 'bias' of ≲0.3 dex, but the paper computes wp(rp) and xi(s) directly; please define how bias is derived from these correlation functions.
  5. [Section 2.3] The weighted correlation function estimator is not described; please specify how the weights f>Lthresh are incorporated (e.g., a weighted Landy-Szalay estimator) and how the mean number density normalization is handled.
  6. [Section 4] The restriction to r_p < 25 Mpc/h is based on a private communication with S. Eftekharzadeh; please provide a public reference or a documented analysis of the systematic issue to make the cut reproducible.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: Trinity's quasar correlation functions are an out-of-sample prediction; the only flagged inconsistency is a parenthetical mention of galaxy correlation functions, which does not reduce the prediction to its inputs.

full rationale

The paper's derivation chain is: take the best-fit Trinity model (Zhang et al. 2023b), which was constrained by galaxy stellar mass functions, SMBH-bulge relation, quasar luminosity functions, and AGN occupation fractions; apply it to MDPL2 halos to obtain the probability f>L_thresh(M_h,z) that a halo hosts an AGN above a luminosity threshold; compute wp and xi(s) by weighting halos with f. No quasar clustering measurement appears in the likelihood, so the comparison in Figures 1-4 is an out-of-sample prediction. The choice L_thresh=1e46 erg/s is justified by the reported typical luminosities of the observed samples and the observationally weak luminosity dependence; Appendix A plots luminosity-binned data, so the comparison is not forced by fitting the threshold to the data. I flag one internal inconsistency: Section 2.3's parenthetical 'galaxy number densities and correlation functions (giving P(M*|Mh,z))' conflicts with the abstract and Section 2.2, which list galaxy number densities but not galaxy correlation functions. If galaxy correlation functions were used, the quasar prediction inherits information from galaxy clustering, weakening the 'no correlation functions at all' framing; however, it remains independent of quasar clustering and is not equal by construction to any fitted quantity. The model is self-cited, but that is standard use of a published model; no uniqueness theorem or ansatz is imported. Hence no circular step.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The prediction rests on the Trinity model's luminosity distribution, the MDPL2 simulation, and the assumption that a single bolometric threshold represents observed quasar samples. No new physical entities are introduced.

free parameters (2)
  • Redshift-space velocity scatter = 700 km/s
    Added to model predictions in Figures 3-4 to match observed small-scale downturn in xi(s); motivated by Croom et al. (2005) but not derived from the model.
  • Bolometric luminosity threshold L_thresh = 10^46 erg/s
    Chosen to approximate the typical luminosity of quasars in the observed samples (Ross et al. 2009); affects the amplitude of predicted clustering.
assumptions (4)
  • domain assumption Flat LambdaCDM cosmology with h=0.67, Omega_m=0.307, Omega_L=0.693, n=0.96, sigma8=0.823.
    Adopted from Planck 2016 and used by MDPL2; standard cosmology assumption.
  • domain assumption The MDPL2 simulation with Rockstar halo finder and Consistent Trees provides a faithful halo population and clustering on scales 0.1-25 Mpc/h.
    The prediction is based on a single N-body simulation; assumes no significant resolution or sample variance effects.
  • domain assumption The best-fit Trinity model is representative of the posterior distribution.
    The paper uses one set of parameters from Zhang et al. (2023b) and does not propagate model uncertainty.
  • domain assumption The Trinity luminosity distribution P(L|Mh,z) from the best-fit model is correct.
    The clustering weights in Eq. (1) depend entirely on this distribution; if it is wrong, the predicted clustering is wrong. The paper tests this indirectly.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Trinity VII. Predictions for the Observable Correlation Functions of Accreting Black Holes." pith.science (2026). https://pith.science/paper/J7PSRT7B

@misc{pith2026250605612,
  author       = {Pith},
  title        = {Pith review of: Trinity VII. Predictions for the Observable Correlation Functions of Accreting Black Holes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/J7PSRT7B}},
  note         = {Machine review of arXiv:2506.05612}
}
abstract

The quasar correlation function assesses the occurrence of quasar pairs as a function of separation, which is strongly influenced by quasar host halo masses. The empirical Trinity model recently inferred the redshift-dependent relationship between supermassive black hole (SMBH) mass, galaxy mass, and halo mass, using constraints other than correlation functions (e.g., quasar luminosity functions, active galactic nuclei occupation fractions, and SMBH mass-bulge mass relations). Hence, comparing the predicted quasar correlation functions from Trinity to real observations is an important test of Trinity's inferred SMBH -- halo relation. In this work, we use a compilation of observed two-point projected and redshift-space correlation functions from $0 \leq z \leq 3.5$. We find that Trinity accurately predicts quasar correlation functions within observed error bars, although observations do not have much constraining power at lower redshifts due to smaller observable volumes and lower quasar number densities. This finding is consistent with Trinity having the correct placement of quasars within their host galaxies and dark matter halos, without requiring quasar clustering constraints during model fitting. Using Trinity, we also predict the clustering as a function of quasar bolometric luminosity, finding that existing survey uncertainties are too large to show measurable differences ($\lesssim 0.3$ dex change in bias for $10^{42}$ erg s$^{-1}$ compared to $10^{46}$ erg s$^{-1}$ SMBHs across redshifts). This fact arises because most SMBH growth (and hence quasar luminosity) occurs in halos in a similar mass range ($10^{12}-10^{13} M_\odot$).

Figures

Figures reproduced from arXiv: 2506.05612 by the authors.

Figure 1
Figure 1. — The two-point projected correlation function, 𝑤𝑝, for 𝑧 = 0 − 2 in Δ𝑧 = 0.5 bins. Trinity predictions are shown as the black solid line, with observations shown as symbols. Observations with > 2 dex uncertainties are shown in transparent hues so that more precise measurements stand out visually. 10−1 100 101 102 rp [Mpc/h] 10−2 10−1 100 101 102 103 w p(r p) [Mpc/h] Trinity, 1046 erg s−1 Ross+2009, z = 2.02-2.20 Ef… view at source ↗
Figure 2
Figure 2. — The two-point projected correlation function, 𝑤𝑝, for 𝑧 = 2 − 3.5 in Δ𝑧 = 0.5 bins. Trinity predictions are shown as the black solid line, with observations shown as symbols. Observations with > 2 dex uncertainties are shown in lighter colors so that more precise measurements stand out visually. tice be selecting quasar samples with very different bolometric luminosity distributions. Nonetheless, the observational… view at source ↗
Figure 3
Figure 3. — The 3D redshift-space correlation function, 𝜉𝑠, for 𝑧 = 0 − 2 in Δ𝑧 = 0.5 bins. Trinity predictions are shown as the black solid line (no redshift-space errors) and the blue solid line (700 km s−1 redshift-space errors), with observations shown as symbols. Observations with > 2 dex uncertainties are shown in lighter colors so that more precise measurements stand out visually. 10−1 100 101 102 s [Mpc/h] 10−2 10−1 1… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: — The 3D redshift-space correlation function, 𝜉𝑠, for 𝑧 = 2−3.5 in Δ𝑧 = 0.5 bins. Trinity predictions are shown as the black solid line (no redshift-space errors) and the blue solid line (700 km s−1 redshift-space errors), with observations shown as symbols. Observatio…
Figure 5
Figure 5. Figure 5: — Top: Luminosity-dependent projected quasar clustering as predicted by Trinity at 𝑧 ∼ 3 and 𝑧 ∼ 5. Bottom: Luminosity-dependent redshift-space quasar clustering as predicted by Trinity at 𝑧 ∼ 3 and 𝑧 ∼ 5. In both cases, lower redshifts are shown in Appendix A; lower r…
Figure 6
Figure 6. Figure 6: — The 3D redshift-space correlation function, 𝜉𝑠 plotted with da Ângela et al. (2008) luminosity-dependent observations.Observations with > 2 dex uncertainties are shown in transparent hues so that more precise measurements stand out visually. APPENDIX A. LUMINOSITY-BI…
Figure 7
Figure 7. Figure 7: — The 3D redshift-space correlation function, 𝜉𝑠 plotted with Chehade et al. (2016) luminosity-dependent observations. Observations with > 2 dex uncertainties are shown in transparent hues so that more precise measurements stand out visually. 10−1 100 101 102 rp [Mpc/h…
Figure 8
Figure 8. Figure 8: —The two-point projected, 𝑤𝑝, and 3D redshift-space correlation functions, 𝜉𝑠 plotted with Eftekharzadeh et al.(2015) luminosity-dependent observations at < 𝑧 = 2.5 >. Observations with > 2 dex uncertainties are shown in transparent hues so that more precise measuremen…
Figure 9
Figure 9. Figure 9: — The two-point projected correlation function, 𝑤𝑝, for TRINITY from 1042 - 1046 erg s−1 . Each luminosity bin is represented by a different color. 10−1 100 101 102 rp [Mpc/h] 10−2 10−1 100 101 102 103 w p(r p) [Mpc/h] Trinity, 1042 erg s−1 Trinity, 1043 erg s−1 Trinit…
Figure 10
Figure 10. Figure 10: — This is an example figure. Captions appear below each figure. Give enough detail for the reader to understand what they’re looking at, but leave detailed discussion to the main body of the text [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]
Figure 11
Figure 11. Figure 11: — The 3D redshift-space correlation function, 𝜉𝑠, for TRINITY from 1042 - 1046 erg s−1 . Each luminosity bin is represented by a different color [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

46 extracted references · 6 canonical work pages

  1. [1]

    L., 2021, @doi [ ] 10.1093/mnras/stab312 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.502.5962A 502, 5962

    Aird J., Coil A. L., 2021, @doi [ ] 10.1093/mnras/stab312 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.502.5962A 502, 5962

    doi:10.1093/mnras/stab312 2021

  2. [2]

    L., Georgakakis A., 2018, @doi [ ] 10.1093/mnras/stx2700 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.474.1225A 474, 1225

    Aird J., Coil A. L., Georgakakis A., 2018, @doi [ ] 10.1093/mnras/stx2700 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.474.1225A 474, 1225

    doi:10.1093/mnras/stx2700 2018

  3. [3]

    S., Wechsler R

    Behroozi P. S., Wechsler R. H., Wu H.-Y., 2013a, @doi [ ] 10.1088/0004-637X/762/2/109 , https://ui.adsabs.harvard.edu/abs/2013ApJ...762..109B 762, 109

    doi:10.1088/0004-637x/762/2/109

  4. [4]

    S., Wechsler R

    Behroozi P. S., Wechsler R. H., Wu H.-Y., Busha M. T., Klypin A. A., Primack J. R., 2013b, @doi [ ] 10.1088/0004-637X/763/1/18 , https://ui.adsabs.harvard.edu/abs/2013ApJ...763...18B 763, 18

    doi:10.1088/0004-637x/763/1/18

  5. [5]

    H., Hearin A

    Behroozi P., Wechsler R. H., Hearin A. P., Conroy C., 2019, @doi [ ] 10.1093/mnras/stz1182 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.488.3143B 488, 3143

    doi:10.1093/mnras/stz1182 2019

  6. [6]

    Bongiorno A., et al., 2012, @doi [ ] 10.1111/j.1365-2966.2012.22089.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.427.3103B 427, 3103

    arXiv 2012

  7. [7]

    Chehade B., et al., 2016, @doi [ ] 10.1093/mnras/stw616 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.459.1179C 459, 1179

    work page doi:10.1093/mnras/stw616 2016

  8. [8]

    Conroy C., White M., 2013, @doi [ ] 10.1088/0004-637X/762/2/70 , https://ui.adsabs.harvard.edu/abs/2013ApJ...762...70C 762, 70

    work page doi:10.1088/0004-637x/762/2/70 2013

Show all 46 references
  1. [9]

    M., et al., 2005, @doi [ ] 10.1111/j.1365-2966.2004.08379.x , https://ui.adsabs.harvard.edu/abs/2005MNRAS.356..415C 356, 415

    Croom S. M., et al., 2005, @doi [ ] 10.1111/j.1365-2966.2004.08379.x , https://ui.adsabs.harvard.edu/abs/2005MNRAS.356..415C 356, 415

    2005

  2. [10]

    J., 2009, @doi [ ] 10.1111/j.1365-2966.2009.14429.x , https://ui.adsabs.harvard.edu/abs/2009MNRAS.394.1109C 394, 1109

    Croton D. J., 2009, @doi [ ] 10.1111/j.1365-2966.2009.14429.x , https://ui.adsabs.harvard.edu/abs/2009MNRAS.394.1109C 394, 1109

    2009

  3. [11]

    S., et al., 2016, @doi [ ] 10.3847/0004-6256/151/2/44 , https://ui.adsabs.harvard.edu/abs/2016AJ....151...44D 151, 44

    Dawson K. S., et al., 2016, @doi [ ] 10.3847/0004-6256/151/2/44 , https://ui.adsabs.harvard.edu/abs/2016AJ....151...44D 151, 44

    2016 doi

  4. [12]

    Eftekharzadeh S., et al., 2015, @doi [ ] 10.1093/mnras/stv1763 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.453.2779E 453, 2779

    2015 doi

  5. [13]

    J., et al., 2011, @doi [ ] 10.1088/0004-6256/142/3/72 , https://ui.adsabs.harvard.edu/abs/2011AJ....142...72E 142, 72

    Eisenstein D. J., et al., 2011, @doi [ ] 10.1088/0004-6256/142/3/72 , https://ui.adsabs.harvard.edu/abs/2011AJ....142...72E 142, 72

    2011 doi

  6. [14]

    arXiv:2304.06658

    Harikane Y., Nakajima K., Ouchi M., Umeda H., Isobe Y., Ono Y., Xu Y., Zhang Y., 2023, @doi [arXiv e-prints] 10.48550/arXiv.2304.06658 , https://ui.adsabs.harvard.edu/abs/2023arXiv230406658H p. arXiv:2304.06658

    2023 doi arXiv

  7. [15]

    H \"a ring N., Rix H.-W., 2004, @doi [ ] 10.1086/383567 , https://ui.adsabs.harvard.edu/abs/2004ApJ...604L..89H 604, L89

    2004 doi

  8. [16]

    F., Hernquist L., Cox T

    Hopkins P. F., Hernquist L., Cox T. J., Kere s D., 2008, @doi [ ] 10.1086/524362 , https://ui.adsabs.harvard.edu/abs/2008ApJS..175..356H 175, 356

    2008 doi

  9. [17]

    Klypin A., Yepes G., Gottl \"o ber S., Prada F., He S., 2016, @doi [ ] 10.1093/mnras/stw248 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.457.4340K 457, 4340

    2016 doi

  10. [18]

    C., 2013, @doi [ ] 10.1146/annurev-astro-082708-101811 , https://ui.adsabs.harvard.edu/abs/2013ARA&A..51..511K 51, 511

    Kormendy J., Ho L. C., 2013, @doi [ ] 10.1146/annurev-astro-082708-101811 , https://ui.adsabs.harvard.edu/abs/2013ARA&A..51..511K 51, 511

    2013 doi

  11. [19]

    G., Eisenstein D

    Krolewski A. G., Eisenstein D. J., 2015, @doi [ ] 10.1088/0004-637X/803/1/4 , https://ui.adsabs.harvard.edu/abs/2015ApJ...803....4K 803, 4

    2015 doi

  12. [20]

    Laurent P., et al., 2017, @doi [ ] 10.1088/1475-7516/2017/07/017 , https://ui.adsabs.harvard.edu/abs/2017JCAP...07..017L 2017, 017

    2017 doi

  13. [21]

    Li J., et al., 2021, @doi [ ] 10.3847/1538-4357/ac2301 , https://ui.adsabs.harvard.edu/abs/2021ApJ...922..142L 922, 142

    2021 doi

  14. [22]

    J., Ma C.-P., 2013, @doi [ ] 10.1088/0004-637X/764/2/184 , https://ui.adsabs.harvard.edu/abs/2013ApJ...764..184M 764, 184

    McConnell N. J., Ma C.-P., 2013, @doi [ ] 10.1088/0004-637X/764/2/184 , https://ui.adsabs.harvard.edu/abs/2013ApJ...764..184M 764, 184

    2013 doi

  15. [23]

    P., Naab T., White S

    Moster B. P., Naab T., White S. D. M., 2018, @doi [ ] 10.1093/mnras/sty655 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.477.1822M 477, 1822

    2018 doi

  16. [24]

    P., 2017, @doi [ ] 10.1146/annurev-astro-081913-040019 , https://ui.adsabs.harvard.edu/abs/2017ARA&A..55...59N 55, 59

    Naab T., Ostriker J. P., 2017, @doi [ ] 10.1146/annurev-astro-081913-040019 , https://ui.adsabs.harvard.edu/abs/2017ARA&A..55...59N 55, 59

    2017 doi

  17. [25]

    Planck Collaboration et al., 2016, @doi [ ] 10.1051/0004-6361/201525830 , https://ui.adsabs.harvard.edu/abs/2016A&A...594A..13P 594, A13

    2016 doi

  18. [26]

    C., et al., 2018, @doi [ ] 10.3847/1538-4357/aabd7f , https://ui.adsabs.harvard.edu/abs/2018ApJ...858..110P 858, 110

    Powell M. C., et al., 2018, @doi [ ] 10.3847/1538-4357/aabd7f , https://ui.adsabs.harvard.edu/abs/2018ApJ...858..110P 858, 110

    2018 doi

  19. [27]

    C., Krumpe M., Coil A., Miyaji T., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2403.03978 , https://ui.adsabs.harvard.edu/abs/2024arXiv240303978P p

    Powell M. C., Krumpe M., Coil A., Miyaji T., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2403.03978 , https://ui.adsabs.harvard.edu/abs/2024arXiv240303978P p. arXiv:2403.03978

    2024 doi arXiv

  20. [29]

    Rodr \' guez-Puebla A., Behroozi P., Primack J., Klypin A., Lee C., Hellinger D., 2016, @doi [ ] 10.1093/mnras/stw1705 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.462..893R 462, 893

    2016 doi

  21. [30]

    P., et al., 2009, @doi [ ] 10.1088/0004-637X/697/2/1634 , https://ui.adsabs.harvard.edu/abs/2009ApJ...697.1634R 697, 1634

    Ross N. P., et al., 2009, @doi [ ] 10.1088/0004-637X/697/2/1634 , https://ui.adsabs.harvard.edu/abs/2009ApJ...697.1634R 697, 1634

    2009 doi

  22. [31]

    P., et al., 2007, @doi [ ] 10.1086/518474 , https://ui.adsabs.harvard.edu/abs/2007AJ....134..102S 134, 102

    Schneider D. P., et al., 2007, @doi [ ] 10.1086/518474 , https://ui.adsabs.harvard.edu/abs/2007AJ....134..102S 134, 102

    2007 doi

  23. [32]

    Shankar F., et al., 2020a, @doi [Nature Astronomy] 10.1038/s41550-019-0949-y , https://ui.adsabs.harvard.edu/abs/2020NatAs...4..282S 4, 282

    doi

  24. [33]

    Shankar F., et al., 2020b, @doi [ ] 10.1093/mnras/stz3522 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.493.1500S 493, 1500

    doi

  25. [34]

    Shanks T., et al., 2015, @doi [ ] 10.1093/mnras/stv1130 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.451.4238S 451, 4238

    2015 doi

  26. [35]

    Shen Y., 2009, @doi [ ] 10.1088/0004-637X/704/1/89 , https://ui.adsabs.harvard.edu/abs/2009ApJ...704...89S 704, 89

    2009 doi

  27. [36]

    Shen Y., et al., 2009, @doi [ ] 10.1088/0004-637X/697/2/1656 , https://ui.adsabs.harvard.edu/abs/2009ApJ...697.1656S 697, 1656

    2009 doi

  28. [37]

    A., 2012, @doi [Research in Astronomy and Astrophysics] 10.1088/1674-4527/12/8/004 , https://ui.adsabs.harvard.edu/abs/2012RAA....12..917S 12, 917

    Silk J., Mamon G. A., 2012, @doi [Research in Astronomy and Astrophysics] 10.1088/1674-4527/12/8/004 , https://ui.adsabs.harvard.edu/abs/2012RAA....12..917S 12, 917

    2012 doi

  29. [38]

    J., Croom S

    Smith R. J., Croom S. M., Boyle B. J., Shanks T., Miller L., Loaring N. S., 2005, @doi [ ] 10.1111/j.1365-2966.2005.08870.x , https://ui.adsabs.harvard.edu/abs/2005MNRAS.359...57S 359, 57

    2005

  30. [39]

    S., Dav \'e R., 2015, @doi [ ] 10.1146/annurev-astro-082812-140951 , https://ui.adsabs.harvard.edu/abs/2015ARA&A..53...51S 53, 51

    Somerville R. S., Dav \'e R., 2015, @doi [ ] 10.1146/annurev-astro-082812-140951 , https://ui.adsabs.harvard.edu/abs/2015ARA&A..53...51S 53, 51

    2015 doi

  31. [40]

    L., Robertson B

    Tinker J. L., Robertson B. E., Kravtsov A. V., Klypin A., Warren M. S., Yepes G., Gottl \"o ber S., 2010, @doi [ ] 10.1088/0004-637X/724/2/878 , https://ui.adsabs.harvard.edu/abs/2010ApJ...724..878T 724, 878

    2010 doi

  32. [41]

    Vogelsberger M., Marinacci F., Torrey P., Puchwein E., 2020, @doi [Nature Reviews Physics] 10.1038/s42254-019-0127-2 , https://ui.adsabs.harvard.edu/abs/2020NatRP...2...42V 2, 42

    2020 doi

  33. [42]

    H., Tinker J

    Wechsler R. H., Tinker J. L., 2018, @doi [ ] 10.1146/annurev-astro-081817-051756 , https://ui.adsabs.harvard.edu/abs/2018ARA&A..56..435W 56, 435

    2018 doi

  34. [43]

    Yang J., et al., 2023, @doi [ ] 10.3847/1538-4365/acf99b , https://ui.adsabs.harvard.edu/abs/2023ApJS..269...27Y 269, 27

    2023 doi

  35. [44]

    G., et al., 2000, @doi [ ] 10.1086/301513 , https://ui.adsabs.harvard.edu/abs/2000AJ....120.1579Y 120, 1579

    York D. G., et al., 2000, @doi [ ] 10.1086/301513 , https://ui.adsabs.harvard.edu/abs/2000AJ....120.1579Y 120, 1579

    2000 doi

  36. [45]

    F., 2023a, @doi [arXiv e-prints] 10.48550/arXiv.2305.19315 , https://ui.adsabs.harvard.edu/abs/2023arXiv230519315Z p

    Zhang H., Behroozi P., Volonteri M., Silk J., Fan X., Aird J., Yang J., Hopkins P. F., 2023a, @doi [arXiv e-prints] 10.48550/arXiv.2305.19315 , https://ui.adsabs.harvard.edu/abs/2023arXiv230519315Z p. arXiv:2305.19315

    doi arXiv

  37. [46]

    F., Yang J., Aird J., 2023b, @doi [ ] 10.1093/mnras/stac2633 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.518.2123Z 518, 2123

    Zhang H., Behroozi P., Volonteri M., Silk J., Fan X., Hopkins P. F., Yang J., Aird J., 2023b, @doi [ ] 10.1093/mnras/stac2633 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.518.2123Z 518, 2123

    doi

  38. [47]

    da \^A ngela J., et al., 2008, @doi [ ] 10.1111/j.1365-2966.2007.12552.x , 383, 565

    2008

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.