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REVIEW 3 major objections 4 minor 54 references

The Impact of Galaxy-halo Size Relations on Galaxy Clustering Signals

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper argues that a simple linear galaxy-size–halo-radius model, when combined with peak-mass abundance matching, implicitly encodes halo formation time and thereby reproduces the observed size-split clustering pattern without…

desk verdict Useful model forensics: explains the K13 size-split clustering via implicit assembly bias, with a caveat that the high-mass cancellation leans on the adopted SHMR. read the letter →

arxiv 2411.13484 v2 pith:OAKZUQK3 submitted 2024-11-20 astro-ph.GA

Joshua B. Hill , Yao-Yuan Mao (U of Utah) This is my paper · ORCID
classification astro-ph.GA
keywords galaxysizeshaloassemblybiassubhaloabundancematchingclusteringdarkmatterhalosstellar-to-halomassrelationprojectedcorrelationfunctionK13sizemodel
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

This paper tries to explain why a deliberately simple recipe for galaxy sizes—make the half-light radius a fixed fraction of a halo's virial radius at peak mass—reproduces observed clustering differences between small and large galaxies at fixed stellar mass. The explanation is that the recipe is not as simple as it looks: because the virial mass–radius relation depends on cosmic time, using the radius at peak mass makes a galaxy's size sensitive to when the halo reached peak mass. Small galaxies preferentially sit in earlier-forming halos, whose clustering is boosted by halo assembly bias. At high stellar mass this assembly-bias boost is balanced by ordinary halo bias favoring large galaxies in more massive halos. The consequence is that matching clustering data forces small and large galaxies to differ in halo assembly history, not just halo mass.

What carries the argument

The central object is the time-dependent virial mass–radius relation, $M_{\rm peak} = (4\pi/3)\,r_{M_{\rm peak}}^3\,\Delta_{\rm vir}(a_{M_{\rm peak}})\,\rho_{\rm crit}(a_{M_{\rm peak}})$, together with the size prescription $r_{1/2}=0.01\,r_{M_{\rm peak}}$. Because $\Delta_{\rm vir}$ and $\rho_{\rm crit}$ depend on the scale factor at peak mass, this pair of equations converts a halo's assembly time into its assigned galaxy size at fixed peak mass. The mechanism carries the argument by showing that the size split at fixed stellar mass is also a split in $a_{M_{\rm peak}}$, which is the property that halo assembly bias acts on.

What would settle it

A concrete calculation is to recompute the high-mass size-split clustering after replacing the adopted high-mass stellar mass function with one whose slope is shifted by its quoted uncertainty; if the convergence of large- and small-galaxy clustering disappears or moves by more than the clustering error bars, the mechanism's reliance on the stellar-to-halo mass relation is falsified. A direct observational check is to measure the size-split correlation function at $\log(M_\star/M_\odot)\gtrsim 11$ with precision high enough to confirm the predicted convergence.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the linear size model of Kravtsov (2013), in which $r_{1/2}=0.01\,r_{M_{\rm peak}}$, implicitly depends on halo formation history when stellar masses are assigned by subhalo abundance matching on $M_{\rm peak}$. The time-dependent spherical-overdensity relation means that among halos of the same $M_{\rm peak}$, those that reached peak mass earlier have smaller $r_{M_{\rm peak}}$ and hence smaller modeled galaxies. Since earlier-forming halos are more clustered at fixed mass, small galaxies are predicted to be more clustered at lower stellar masses, and at higher stellar masses that trend is offset by the larger $M_{\rm peak}$ of large galaxies as the stellar-to-halo mass relation flattens. The paper also finds that replacing $r_{M_{\rm peak}}$ with present-day $r_{\rm vir}$ changes little, because tidal stripping introduces a similar assembly-history dependence. The conclusion is that any size model matching the observed size-split clustering must effectively separate galaxies by halo assembly history, and clustering alone cannot identify which halo property controls size.

Load-bearing premise

The load-bearing premise is that the abundance-matched stellar-to-halo mass relation, especially its high-mass slope, is accurate; if the high-mass slope is wrong, the $M_{\rm peak}$ distributions of large and small galaxies at fixed stellar mass shift, and the predicted cancellation between halo bias and assembly bias at high stellar mass fails.

Editorial extensions

If this is right

  • At fixed stellar mass, small modeled galaxies occupy halos with earlier $a_{M_{\rm peak}}$ at all four mass thresholds, so the size-split samples differ in assembly history even though the size model never uses formation time.
  • At low stellar mass the relative halo bias between size-split samples is weak because the stellar-to-halo mass relation is steep, so the clustering gap is dominated by assembly bias.
  • At high stellar mass the stellar-to-halo mass relation flattens, large galaxies occupy more massive halos, and the resulting halo bias offsets assembly bias, making large and small galaxies cluster similarly.
  • Using present-day $r_{\rm vir}$ instead of $r_{M_{\rm peak}}$ gives nearly identical clustering and size–mass relations because the amount of tidal stripping is strongly correlated with $a_{M_{\rm peak}}$.
  • If assembly bias is artificially removed by selecting halos with $a_{M_{\rm peak}}=1$, large galaxies cluster slightly more than small galaxies at all stellar masses, confirming that assembly bias drives the low-mass gap.

Reading between the lines

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

  • One testable extension is to recompute the predicted size-split clustering after perturbing the high-mass slope of the adopted stellar-to-halo mass relation; the stellar mass where the clustering gap closes would shift, allowing existing surveys to test the mechanism.
  • The near-degeneracy between the $r_{M_{\rm peak}}$ and $r_{\rm vir}$ models suggests that any secondary halo property strongly correlated with $a_{M_{\rm peak}}$, such as concentration, can substitute for formation time in a size model while leaving clustering predictions nearly unchanged, so clustering alone cannot break that degeneracy.
  • A direct observational test would measure size segregation in overdense environments: the model predicts that, at fixed stellar mass, small galaxies should be more abundant than large galaxies in dense regions, which can be checked with group catalogs and redshift surveys.
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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. This paper addresses a puzzle in the galaxy–halo connection: why a simple linear galaxy-size–halo-radius model (Kravtsov 2013, as used by Hearin et al. 2019) reproduces the observed size-split galaxy clustering pattern even though it contains no explicit halo formation-time dependence. Using the VSMDPL simulation and the H19 modeling pipeline, the authors show that when stellar masses are assigned via subhalo abundance matching with M_peak and sizes are assigned with r_Mpeak, the size model implicitly encodes the halo formation scale factor a_Mpeak through the time-dependent M_vir–r_vir relation. As a result, at fixed stellar/halo mass, smaller galaxies preferentially occupy earlier-forming halos, injecting halo assembly bias into the clustering signal. The paper argues that at low stellar masses this assembly bias makes small galaxies more clustered than large ones, while at high stellar masses the shallow slope of the abundance-matched SHMR separates the M_peak distributions of small and large galaxies, so that halo bias partially cancels the assembly bias and the clustering gap shrinks. The authors further show that an r_vir-based size model produces nearly identical clustering and size–mass relations, and they discuss the difficulty of identifying the specific halo property controlling galaxy size from clustering alone.

Significance. If the mechanism identified here is correct, the paper provides a clean explanation of a previously puzzling result: the success of the simple K13 size model does not imply that galaxy sizes are directly governed by halo radius alone, because the abundance-matching step smuggles in a formation-time dependence. The control experiment in Appendix A (restricting to a_Mpeak = 1 and reweighting to preserve M_peak distributions) is a strong, targeted test that supports the assembly-bias interpretation, and the model is not circular: the size-model constant and abundance-matching scatter are inherited from prior work, and the clustering gap is an output, not an input. The demonstration that r_Mpeak and r_vir models are nearly degenerate in both clustering and size–mass relations is a useful caution for the field. However, the central explanation of the high-mass convergence depends on the adopted SHMR, and the paper does not quantify how sensitive this conclusion is to that external input.

major comments (3)
  1. [§3.2, §3.3, and Fig. 3] The explanation of the high-mass convergence relies on the M_peak distributions of small and large galaxies separating at high stellar mass (right panel of Fig. 3). This separation is a consequence of the shallow high-mass slope of the SHMR produced by the abundance-matching procedure of §2.2.1 with the Moustakas et al. (2013) and Mortlock et al. (2011) stellar mass functions and a fixed 0.2 dex scatter. The authors do not test how a steeper high-mass SHMR (e.g., Behroozi et al. 2019) or a larger scatter would change the M_peak distributions and thereby weaken the halo-bias cancellation. Without such a sensitivity test, the claim that the K13 model reproduces the observed size-split clustering pattern is conditional on the adopted external SHMR.
  2. [Fig. 2 and §3] Figure 2 shows no error bars on the mock clustering measurements, and the paper does not display the SDSS data against which the model is said to match 'reasonably well'; the comparison is only asserted through H19. Since the central narrative turns on the presence and disappearance of the clustering gap between small and large galaxies, the authors should provide a direct quantitative comparison or at least an estimate of the uncertainty (e.g., jackknife or bootstrap) so that the reader can judge whether the reported gap is significant and whether the claimed match to observations holds.
  3. [§4.1, summary] The conclusion that 'small galaxies have to occupy halos that form early' is stated as a general inference in §4.1 and the summary, but the argument as presented applies within the specific assumptions of the K13/H19 size model: if one relaxes the premise that galaxy size traces halo radius at fixed stellar mass (e.g., allowing morphology or other baryonic effects to set size), the dichotomy between 'more massive halo' and 'earlier-forming halo' is not exhaustive. The authors should soften this claim or explicitly limit it to the class of models considered here.
minor comments (4)
  1. [§2.2.2] Throughout this section the term 'viral radius' should be 'virial radius' (e.g., in the sentence defining r_1/2 = 0.01 r_vir).
  2. [§5] The summary refers to the 'shallower SMHR' at high stellar mass; the abbreviation should be SHMR for consistency with the rest of the paper.
  3. [§2.1] The simulation name is written as 'VSDMPL' in the text but later as 'VSMDPL'; please use one consistent spelling.
  4. [§4.2] The statement that the predicted size evolution 'appears to be greater than one would expect' is not supported by a quantitative comparison to the cited observational constraints (Huang et al. 2017; Martorano et al. 2024); adding a brief quantitative statement would strengthen the point.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the size- and mass-assignment parameters are fixed from prior work, and the size-split clustering gap is an output rather than a fitted target.

full rationale

The paper's central derivation is not circular. The key mechanism in Section 3.1 is that using M_peak for abundance matching and r_Mpeak for the size model introduces an implicit dependence on a_Mpeak: the M_vir-r_vir relation of Equation 2 depends on scale factor, so at fixed M_peak an earlier a_Mpeak gives a smaller r_Mpeak and therefore a smaller assigned galaxy radius. This is a direct, self-contained consequence of the model definitions, not an assumption of the conclusion. The paper quotes the reduction explicitly: 'Since r_Mpeak increases as a_Mpeak increases, the halo with an earlier a_Mpeak will have a smaller r_Mpeak than the later-forming halo. Recall that Equation 2 (the M_vir-r_vir relation) has a time dependence, which in turn introduces the time dependence into Equation 1.' Nothing in this step is fitted to the clustering signal; it follows from the adopted size relation and the simulation's halo histories. The clustering gap between small and large galaxies is an output of the model, not an input: the size proportionality constant (0.01) and the abundance-matching scatter (0.2 dex) are inherited from K13 and H19 and held fixed, and the paper does not tune any parameter to match the observed size-split clustering. The high-redshift predictions in Section 4.2 and the r_vir comparison in Section 3.4 are also forward predictions from the same fixed recipe, and the Appendix A control (removing assembly bias by selecting a_Mpeak = 1 and reweighting M_peak) is an independent check of the causal decomposition. The paper's self-citations (Mao 2022 for the AbundanceMatching code, Mao et al. 2018 for secondary halo bias) are ancillary and not load-bearing: the central argument does not reduce to those citations, and the invoked halo assembly bias phenomenon is independently established in the cited external literature (e.g., Gao et al. 2005; Wechsler et al. 2006). The reviewer's concern that the high-mass convergence depends on the adopted SHMR slope is a sensitivity/correctness caveat about external inputs, not a circularity: the SHMR is not derived from the clustering being explained. Overall, the derivation chain is self-contained against the simulation and fixed external calibrations, and no step equates a fitted parameter with a predicted quantity or imports a uniqueness result from the authors' prior work.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The analysis is conditional on the simulation reproducing halo assembly bias, on the halo catalogs' Mpeak and a_Mpeak being reliable, on the abundance-matched SHMR and adopted stellar mass functions being accurate, and on the H19 size-split clustering pattern being a genuine observational signal. No new entities are introduced, and the only free numerical inputs are inherited from prior work.

free parameters (2)
  • K13 size proportionality constant = 0.01
    Inherited from Kravtsov 2013 and fixed at all redshifts. It does not affect the median-based small/large split, so it is not load-bearing for the clustering pattern.
  • Subhalo abundance matching scatter = 0.2 dex
    Adopted from Hearin et al. 2019. It broadens the Mpeak distributions at fixed stellar mass and influences the relative halo bias between size-split samples.
assumptions (5)
  • domain assumption The VSMDPL gravity-only N-body simulation with Planck cosmology reproduces the halo assembly bias and halo bias statistics used in the analysis.
    Section 2.1; the central mechanism requires that assembly bias in simulated halos behaves as assumed.
  • domain assumption Rockstar and ConsistentTrees catalogs correctly identify halos, subhalos, Mpeak, and a_Mpeak values on each main branch.
    Sections 2.1 and 3.1; Figures 3 and 4 depend on a_Mpeak as a reliable formation-time proxy.
  • domain assumption Subhalo abundance matching using Mpeak with 0.2 dex scatter and the adopted stellar mass functions produces a stellar-to-halo mass relation accurate enough for the conclusions.
    Section 2.2.1; the high-mass SHMR slope controls the halo-bias cancellation in Section 3.2.
  • domain assumption The observed size-split clustering pattern reported by H19 (small galaxies more clustered at low stellar mass, similar clustering at high stellar mass) is a real constraint that the model should reproduce.
    Introduction and Section 3; the explanation is built to match this pattern.
  • domain assumption The K13 linear size relation, r1/2 = 0.01 r_Mpeak or r_vir, is a plausible enough model class to serve as the testbed.
    Section 2.2.2; the conclusions are conditional on this model class, not on its independent validity.

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Cite this review

Pith. "Pith review of The Impact of Galaxy-halo Size Relations on Galaxy Clustering Signals." pith.science (2026). https://pith.science/paper/OAKZUQK3

@misc{pith2026241113484,
  author       = {Pith},
  title        = {Pith review of: The Impact of Galaxy-halo Size Relations on Galaxy Clustering Signals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OAKZUQK3}},
  note         = {Machine review of arXiv:2411.13484}
}
read the original abstract

Galaxies come in different sizes and morphologies, and these differences are thought to correlate with properties of their underlying dark matter halos. However, identifying the specific halo property that controls the galaxy size is a challenging task, especially because most halo properties depend on one another. In this work, we demonstrate this challenge by studying how the galaxy-halo size relations impact the galaxy clustering signals. We investigate the reason that a simple linear relation model, which prescribes that the galaxy size is linearly proportional to the dark matter halo's virial radius, can still produce clustering signals that match the observational data reasonably well. We find that this simple linear relation model for galaxy sizes, when combined with the subhalo abundance matching technique, introduces an implicit dependence on the halo formation history. As a result, the effect of halo assembly bias enters the resulting galaxy clustering, especially at lower stellar masses, producing a clustering signal that resembles the observed one. At higher stellar masses, the effect of halo assembly bias weakens and is partially canceled out by the effect of halo bias, and the clustering of large and small galaxies becomes more similar. This combined effect implies that small and large galaxies not only occupy halos of different masses, but they must also occupy halos of different assembly histories. Our study highlights the challenge of identifying a particular halo property that controls galaxy sizes through constraints from galaxy clustering alone.

Figures

Figures reproduced from arXiv: 2411.13484 by the authors.

Figure 1
Figure 1. Median stellar-to-halo mass relation for model-predicted small (red-filled circles) and large (blue-filled squares) galaxies. The designations of small and large galaxies are described in Section 2.3. Each point shows the median stellar mass (𝑀★) and peak halo mass (𝑀peak) in each 𝑀peak bin, with the error bars showing 1𝜎 of 𝑀★ and 𝑀peak distributions in that bin. The four horizontal dotted lines denote the four 𝑀★ … view at source ↗
Figure 2
Figure 2. Projected two-point (galaxy–galaxy) correlation function, 𝑤𝑝 (𝑟𝑝 ), for various galaxy subsamples. Here 𝑤𝑝 and 𝑟𝑝 are both shown in comoving distances. The two rows show 𝑤𝑝 (𝑟𝑝 ) at two redshifts: 𝑧 = 0 (upper) and 𝑧 = 3 (lower). The four columns show 𝑤𝑝 (𝑟𝑝 ) of four galaxy samples corresponding to different stellar mass thresholds (from left to right): log (𝑀★/𝑀⊙ ) ≥ 9.75, 10.25, 10.75, and 11. The color and thick… view at source ↗
Figure 3
Figure 3. Distributions of 𝑎𝑀peak (left) and 𝑀peak (right) of small (red) and large (blue) galaxies in bins of stellar mass, log (𝑀★/𝑀⊙ ), of [9.75, 10.25), [10.25, 10.75), [10.75, 11), and ≥ 11. The distribution (of 𝑎𝑀peak or 𝑀peak) is shown vertically as a violin plot, with a box plot overlaid to show the median, inner quartiles, and 1.5 times the interquartile range (IQR). The difference in 𝑎𝑀peak distributions between sma… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: The time evolution (time shown as scale factor, 𝑎) of halo mass (𝑀vir; upper) and virial radius (𝑟vir; lower) for two halos with the same 𝑀peak but different 𝑎𝑀peak values: 𝑎𝑀peak = 0.641 (red dash-dotted curves) and 1 (blue solid curves). The 𝑟vir values shown are con…
Figure 5
Figure 5. Figure 5: Model-predicted relation between physical half light radius and stellar mass (𝑟1/2–𝑀★ relation) at multiple redshifts (from top to bottom, 𝑧 = 0, 0.5, 1, 2, and 3; also shown as different shades of colors from dark blue to light pink). The corresponding dashed lines de…

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Works this paper leans on

54 extracted references · 14 canonical work pages

  1. [1]

    Gao , author V

    author author L. Gao , author V. Springel , \ and\ author S. D. M. \ White ,\ 10.1111/j.1745-3933.2005.00084.x journal journal \ volume 363 ,\ pages L66 ( year 2005 ) ,\ http://arxiv.org/abs/astro-ph/0506510 arXiv:astro-ph/0506510 [astro-ph] NoStop

    arXiv 2005

  2. [2]

    Matarrese \ and\ author L

    author author S. Matarrese \ and\ author L. Verde ,\ 10.1086/587840 journal journal \ volume 677 ,\ pages L77 ( year 2008 ) ,\ http://arxiv.org/abs/0801.4826 arXiv:0801.4826 [astro-ph] NoStop

    arXiv 2008

  3. [3]

    author author R. H. \ Wechsler \ and\ author J. L. \ Tinker ,\ 10.1146/annurev-astro-081817-051756 journal journal \ volume 56 ,\ pages 435 ( year 2018 ) ,\ http://arxiv.org/abs/1804.03097 arXiv:1804.03097 [astro-ph.GA] NoStop

    arXiv 2018

  4. [4]

    author author B. P. \ Moster , author R. S. \ Somerville , author C. Maulbetsch , author F. C. \ van den Bosch , author A. V. \ Macci \`o , author T. Naab , \ and\ author L. Oser ,\ 10.1088/0004-637X/710/2/903 journal journal \ volume 710 ,\ pages 903 ( year 2010 ) ,\ http://arxiv.org/abs/0903.4682 arXiv:0903.4682 [astro-ph.CO] NoStop

    arXiv

  5. [5]

    Behroozi , author R

    author author P. Behroozi , author R. H. \ Wechsler , author A. P. \ Hearin , \ and\ author C. Conroy ,\ 10.1093/mnras/stz1182 journal journal \ volume 488 ,\ pages 3143 ( year 2019 ) ,\ http://arxiv.org/abs/1806.07893 arXiv:1806.07893 [astro-ph.GA] NoStop

    arXiv 2019

  6. [6]

    author author A. P. \ Hearin \ and\ author D. F. \ Watson ,\ 10.1093/mnras/stt1374 journal journal \ volume 435 ,\ pages 1313 ( year 2013 ) ,\ http://arxiv.org/abs/1304.5557 arXiv:1304.5557 [astro-ph.CO] NoStop

    work page Pith review arXiv 2013

  7. [7]

    author author R. S. \ Somerville , author P. Behroozi , author V. Pandya , author A. Dekel , author S. M. \ Faber , author A. Fontana , author A. M. \ Koekemoer , author D. C. \ Koo , author P. G. \ P \'e rez-Gonz \'a lez , author J. R. \ Primack , author P. Santini , author E. N. \ Taylor , \ and\ author A. van der Wel ,\ 10.1093/mnras/stx2040 journal jo...

    work page Pith review arXiv

  8. [8]

    Analysis of the galaxy size versus stellar mass relation

    author author J. S \'a nchez Almeida ,\ 10.1093/mnras/staa1108 journal journal \ volume 495 ,\ pages 78 ( year 2020 ) ,\ http://arxiv.org/abs/2004.09433 arXiv:2004.09433 [astro-ph.GA] NoStop

    work page Pith review arXiv 2020

Show all 54 references
  1. [9]

    Rodriguez , author A

    author author F. Rodriguez , author A. D. \ Montero-Dorta , author R. E. \ Angulo , author M. C. \ Artale , \ and\ author M. Merch \'a n ,\ 10.1093/mnras/stab1571 journal journal \ volume 505 ,\ pages 3192 ( year 2021 ) ,\ http://arxiv.org/abs/2011.00014 arXiv:2011.00014 [astr...

    2021 arXiv

  2. [10]

    Klein , author J

    author author C. Klein , author J. S. \ Bullock , author J. Moreno , author F. J. \ Mercado , author P. F. \ Hopkins , author R. K. \ Cochrane , \ and\ author J. A. \ Benavides ,\ 10.1093/mnras/stae1505 journal journal \ volume 532 ,\ pages 538 ( year 2024 ) ,\ http://arxiv.or...

    arXiv

  3. [11]

    Du , author H.-C

    author author M. Du , author H.-C. \ Ma , author W.-Y. \ Zhong , author L. C. \ Ho , author S. Liao , \ and\ author Y. Peng ,\ 10.1051/0004-6361/202348989 journal journal \ volume 686 ,\ eid A168 ( year 2024 ) ,\ http://arxiv.org/abs/2403.17313 arXiv:2403.17313 [astro-ph.GA] NoStop

    2024 arXiv

  4. [12]

    Ito , author F

    author author K. Ito , author F. Valentino , author G. Brammer , author A. L. \ Faisst , author S. Gillman , author C. G \'o mez-Guijarro , author K. M. L. \ Gould , author K. E. \ Heintz , author O. Ilbert , author C. K. \ Jespersen , author V. Kokorev , author M. Kubo , auth...

    arXiv

  5. [13]

    Buitrago \ and\ author I

    author author F. Buitrago \ and\ author I. Trujillo ,\ 10.1051/0004-6361/202346133 journal journal \ volume 682 ,\ eid A110 ( year 2024 ) ,\ http://arxiv.org/abs/2311.07656 arXiv:2311.07656 [astro-ph.GA] NoStop

    2024 arXiv

  6. [14]

    author author D. J. \ Prole ,\ 10.1093/mnrasl/slab073 journal journal \ volume 506 ,\ pages L59 ( year 2021 ) ,\ http://arxiv.org/abs/2106.14924 arXiv:2106.14924 [astro-ph.GA] NoStop

    2021 arXiv

  7. [15]

    author author A. V. \ Kravtsov ,\ 10.1088/2041-8205/764/2/L31 journal journal \ volume 764 ,\ eid L31 ( year 2013 ) ,\ http://arxiv.org/abs/1212.2980 arXiv:1212.2980 [astro-ph.CO] NoStop

    2013 arXiv

  8. [16]

    author author A. V. \ Kravtsov , author A. A. \ Berlind , author R. H. \ Wechsler , author A. A. \ Klypin , author S. Gottl \"o ber , author B. Allgood , \ and\ author J. R. \ Primack ,\ 10.1086/420959 journal journal \ volume 609 ,\ pages 35 ( year 2004 ) ,\ http://arxiv.org/...

    arXiv

  9. [17]

    author author R. M. \ Reddick , author R. H. \ Wechsler , author J. L. \ Tinker , \ and\ author P. S. \ Behroozi ,\ 10.1088/0004-637X/771/1/30 journal journal \ volume 771 ,\ eid 30 ( year 2013 ) ,\ http://arxiv.org/abs/1207.2160 arXiv:1207.2160 [astro-ph.CO] NoStop

    2013 arXiv

  10. [18]

    \ Huang , author S

    author author K.-H. \ Huang , author S. M. \ Fall , author H. C. \ Ferguson , author A. van der Wel , author N. Grogin , author A. Koekemoer , author S.-K. \ Lee , author P. G. \ P \'e rez-Gonz \'a lez , \ and\ author S. Wuyts ,\ 10.3847/1538-4357/aa62a6 journal journal \ volu...

    arXiv

  11. [19]

    Desmond \ and\ author R

    author author H. Desmond \ and\ author R. H. \ Wechsler ,\ 10.1093/mnras/stv1978 journal journal \ volume 454 ,\ pages 322 ( year 2015 ) ,\ http://arxiv.org/abs/1506.00169 arXiv:1506.00169 [astro-ph.GA] NoStop

    2015 arXiv

  12. [20]

    author author S. M. \ Fall \ and\ author G. Efstathiou ,\ 10.1093/mnras/193.2.189 journal journal \ volume 193 ,\ pages 189 ( year 1980 ) NoStop

    1980 doi

  13. [21]

    author author R. S. \ Somerville , author P. F. \ Hopkins , author T. J. \ Cox , author B. E. \ Robertson , \ and\ author L. Hernquist ,\ 10.1111/j.1365-2966.2008.13805.x journal journal \ volume 391 ,\ pages 481 ( year 2008 ) ,\ http://arxiv.org/abs/0808.1227 arXiv:0808.1227 ...

    2008

  14. [22]

    author author A. J. \ Benson ,\ 10.1016/j.newast.2011.07.004 journal journal \ volume 17 ,\ pages 175 ( year 2012 ) ,\ http://arxiv.org/abs/1008.1786 arXiv:1008.1786 [astro-ph.CO] NoStop

    2011 arXiv

  15. [23]

    Hearin , author P

    author author A. Hearin , author P. Behroozi , author A. Kravtsov , \ and\ author B. Moster ,\ 10.1093/mnras/stz2251 journal journal \ volume 489 ,\ pages 1805 ( year 2019 ) ,\ http://arxiv.org/abs/1711.10500 arXiv:1711.10500 [astro-ph.GA] NoStop

    2019 arXiv

  16. [24]

    author author F. D. \ Albareti , author C. Allende Prieto , author A. Almeida , author F. Anders , author S. Anderson , author B. H. \ Andrews , author A. Arag \'o n-Salamanca , author M. Argudo-Fern \'a ndez , author E. Armengaud , author E. Aubourg , \ and\ author et al. ,\ ...

    arXiv

  17. [25]

    Jiang , author A

    author author F. Jiang , author A. Dekel , author O. Kneller , author S. Lapiner , author D. Ceverino , author J. R. \ Primack , author S. M. \ Faber , author A. V. \ Macci \`o , author A. A. \ Dutton , author S. Genel , \ and\ author R. S. \ Somerville ,\ 10.1093/mnras/stz195...

    arXiv

  18. [26]

    Behroozi , author A

    author author P. Behroozi , author A. Hearin , \ and\ author B. P. \ Moster ,\ 10.1093/mnras/stab3193 journal journal \ volume 509 ,\ pages 2800 ( year 2022 ) ,\ http://arxiv.org/abs/2101.05280 arXiv:2101.05280 [astro-ph.GA] NoStop

    2022 arXiv

  19. [27]

    author author R. H. \ Wechsler , author A. R. \ Zentner , author J. S. \ Bullock , author A. V. \ Kravtsov , \ and\ author B. Allgood ,\ 10.1086/507120 journal journal \ volume 652 ,\ pages 71 ( year 2006 ) ,\ http://arxiv.org/abs/astro-ph/0512416 arXiv:astro-ph/0512416 [astro...

    2006 arXiv

  20. [28]

    \ Mao , author A

    author author Y.-Y. \ Mao , author A. R. \ Zentner , \ and\ author R. H. \ Wechsler ,\ 10.1093/mnras/stx3111 journal journal \ volume 474 ,\ pages 5143 ( year 2018 ) ,\ http://arxiv.org/abs/1705.03888 arXiv:1705.03888 [astro-ph.CO] NoStop

    2018 arXiv

  21. [29]

    Riebe , author A

    author author K. Riebe , author A. M. \ Partl , author H. Enke , author J. Forero-Romero , author S. Gottl \"o ber , author A. Klypin , author G. Lemson , author F. Prada , author J. R. \ Primack , author M. Steinmetz , \ and\ author V. Turchaninov ,\ 10.1002/asna.201211900 jo...

    doi

  22. [30]

    author author Planck Collaboration , author P. A. R. \ Ade , author N. Aghanim , author C. Armitage-Caplan , author M. Arnaud , author M. Ashdown , author F. Atrio-Barandela , author J. Aumont , author C. Baccigalupi , author A. J. \ Banday , \ and\ author et al. ,\ 10.1051/00...

    arXiv

  23. [31]

    author author P. S. \ Behroozi , author R. H. \ Wechsler , \ and\ author H.-Y. \ Wu ,\ 10.1088/0004-637X/762/2/109 journal journal \ volume 762 ,\ eid 109 ( year 2013 a ) ,\ http://arxiv.org/abs/1110.4372 arXiv:1110.4372 [astro-ph.CO] NoStop

    2013 arXiv

  24. [32]

    author author P. S. \ Behroozi , author R. H. \ Wechsler , author H.-Y. \ Wu , author M. T. \ Busha , author A. A. \ Klypin , \ and\ author J. R. \ Primack ,\ 10.1088/0004-637X/763/1/18 journal journal \ volume 763 ,\ eid 18 ( year 2013 b ) ,\ http://arxiv.org/abs/1110.4370 ar...

    arXiv

  25. [33]

    author author P. S. \ Behroozi , author C. Conroy , \ and\ author R. H. \ Wechsler ,\ 10.1088/0004-637X/717/1/379 journal journal \ volume 717 ,\ pages 379 ( year 2010 ) ,\ http://arxiv.org/abs/1001.0015 arXiv:1001.0015 [astro-ph.CO] NoStop

    2010 arXiv

  26. [34]

    Chaves-Montero , author R

    author author J. Chaves-Montero , author R. E. \ Angulo , author J. Schaye , author M. Schaller , author R. A. \ Crain , author M. Furlong , \ and\ author T. Theuns ,\ 10.1093/mnras/stw1225 journal journal \ volume 460 ,\ pages 3100 ( year 2016 ) ,\ http://arxiv.org/abs/1507.0...

    arXiv

  27. [35]

    author author B. V. \ Lehmann , author Y.-Y. \ Mao , author M. R. \ Becker , author S. W. \ Skillman , \ and\ author R. H. \ Wechsler ,\ 10.3847/1538-4357/834/1/37 journal journal \ volume 834 ,\ eid 37 ( year 2017 ) ,\ http://arxiv.org/abs/1510.05651 arXiv:1510.05651 [astro-p...

    2017 arXiv

  28. [36]

    Moustakas , author A

    author author J. Moustakas , author A. L. \ Coil , author J. Aird , author M. R. \ Blanton , author R. J. \ Cool , author D. J. \ Eisenstein , author A. J. \ Mendez , author K. C. \ Wong , author G. Zhu , \ and\ author S. Arnouts ,\ 10.1088/0004-637X/767/1/50 journal journal \...

    arXiv

  29. [37]

    Mortlock , author C

    author author A. Mortlock , author C. J. \ Conselice , author A. F. L. \ Bluck , author A. E. \ Bauer , author R. Gr \"u tzbauch , author F. Buitrago , \ and\ author J. Ownsworth ,\ 10.1111/j.1365-2966.2011.18357.x journal journal \ volume 413 ,\ pages 2845 ( year 2011 ) ,\ ht...

    2011

  30. [38]

    \ Mao ,\ @noop title AbundanceMatching: Subhalo abundance matching with scatter , \ howpublished Astrophysics Source Code Library, record ascl:2212.016 ( year 2022 ) NoStop

    author author Y.-Y. \ Mao ,\ @noop title AbundanceMatching: Subhalo abundance matching with scatter , \ howpublished Astrophysics Source Code Library, record ascl:2212.016 ( year 2022 ) NoStop

    2022

  31. [39]

    author author P. C. \ Hewett ,\ 10.1093/mnras/201.4.867 journal journal \ volume 201 ,\ pages 867 ( year 1982 ) NoStop

    1982 doi

  32. [40]

    author author A. P. \ Hearin , author D. Campbell , author E. Tollerud , author P. Behroozi , author B. Diemer , author N. J. \ Goldbaum , author E. Jennings , author A. Leauthaud , author Y.-Y. \ Mao , author S. More , author J. Parejko , author M. Sinha , author B. Sip \"o c...

    arXiv

  33. [41]

    Yue , author L

    author author S. Yue , author L. Feng , author W. Ju , author J. Pan , author Z. Huang , author F. Fang , author Z. Li , author Y.-C. \ Cai , \ and\ author W. Zhu ,\ 10.1093/mnras/stae2513 journal journal \ volume 535 ,\ pages 3500 ( year 2024 ) ,\ http://arxiv.org/abs/2408.16...

    arXiv

  34. [42]

    author author R. K. \ Sheth \ and\ author G. Tormen ,\ 10.1046/j.1365-8711.1999.02692.x journal journal \ volume 308 ,\ pages 119 ( year 1999 ) ,\ http://arxiv.org/abs/astro-ph/9901122 arXiv:astro-ph/9901122 [astro-ph] NoStop

    1999

  35. [43]

    Mansfield \ and\ author A

    author author P. Mansfield \ and\ author A. V. \ Kravtsov ,\ 10.1093/mnras/staa430 journal journal \ volume 493 ,\ pages 4763 ( year 2020 ) ,\ http://arxiv.org/abs/1902.00030 arXiv:1902.00030 [astro-ph.CO] NoStop

    2020 arXiv

  36. [44]

    author author R. H. \ Wechsler , author J. S. \ Bullock , author J. R. \ Primack , author A. V. \ Kravtsov , \ and\ author A. Dekel ,\ 10.1086/338765 journal journal \ volume 568 ,\ pages 52 ( year 2002 ) ,\ http://arxiv.org/abs/astro-ph/0108151 arXiv:astro-ph/0108151 [astro-p...

    2002 arXiv

  37. [45]

    \ Mao , author M

    author author Y.-Y. \ Mao , author M. Williamson , \ and\ author R. H. \ Wechsler ,\ 10.1088/0004-637X/810/1/21 journal journal \ volume 810 ,\ eid 21 ( year 2015 ) ,\ http://arxiv.org/abs/1503.02637 arXiv:1503.02637 [astro-ph.CO] NoStop

    2015 arXiv

  38. [46]

    author author P. S. \ Behroozi , author R. H. \ Wechsler , \ and\ author C. Conroy ,\ 10.1088/0004-637X/770/1/57 journal journal \ volume 770 ,\ eid 57 ( year 2013 c ) ,\ http://arxiv.org/abs/1207.6105 arXiv:1207.6105 [astro-ph.CO] NoStop

    2013 arXiv

  39. [47]

    Martorano , author A

    author author M. Martorano , author A. van der Wel , author M. Baes , author E. F. \ Bell , author G. Brammer , author M. Franx , \ and\ author A. Nersesian ,\ 10.3847/1538-4357/ad5c6a journal journal \ volume 972 ,\ eid 134 ( year 2024 ) ,\ http://arxiv.org/abs/2406.17756 arX...

    arXiv

  40. [48]

    author author C. R. \ Harris , author K. J. \ Millman , author S. J. \ van der Walt , author R. Gommers , author P. Virtanen , author D. Cournapeau , author E. Wieser , author J. Taylor , author S. Berg , author N. J. \ Smith , author R. Kern , author M. Picus , author S. Hoye...

    arXiv

  41. [49]

    Virtanen , author R

    author author P. Virtanen , author R. Gommers , author T. E. \ Oliphant , author M. Haberland , author T. Reddy , author D. Cournapeau , author E. Burovski , author P. Peterson , author W. Weckesser , author J. Bright , author S. J. \ van der Walt , author M. Brett , author J....

    arXiv

  42. [50]

    author author J. D. \ Hunter ,\ 10.1109/MCSE.2007.55 journal journal Computing in Science and Engineering \ volume 9 ,\ pages 90 ( year 2007 ) NoStop

    2007 doi

  43. [51]

    Perez \ and\ author B

    author author F. Perez \ and\ author B. E. \ Granger ,\ 10.1109/MCSE.2007.53 journal journal Computing in Science and Engineering \ volume 9 ,\ pages 21 ( year 2007 ) NoStop

    2007 doi

  44. [52]

    Kluyver , author B

    author author T. Kluyver , author B. Ragan-Kelley , author F. P \'e rez , author B. Granger , author M. Bussonnier , author J. Frederic , author K. Kelley , author J. Hamrick , author J. Grout , author S. Corlay , author P. Ivanov , author D. Avila , author S. Abdalla , author...

    doi

  45. [53]

    author author The pandas development Team ,\ 10.5281/zenodo.3509134 title pandas-dev/pandas: Pandas , \ ( year 2024 ) NoStop

    2024 doi

  46. [54]

    author author C. T. \ Lee , author J. R. \ Primack , author P. Behroozi , author A. Rodr \' guez-Puebla , author D. Hellinger , \ and\ author A. Dekel ,\ 10.1093/mnras/sty2538 journal journal \ volume 481 ,\ pages 4038 ( year 2018 ) ,\ http://arxiv.org/abs/1711.10620 arXiv:171...

    arXiv

Pith tools

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