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REVIEW 2 major objections 4 minor 95 references

Testing the Accuracy of Halo Occupation Distribution Modelling using Hydrodynamic Simulations

T0 review · 2 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A simple five-parameter galaxy-halo recipe works for bright galaxies after correcting halo masses for baryons, but faint galaxies need extra bias parameters.

desk verdict A systematic and useful HOD stress test whose main claims hold up, though the key mass-correction robustness check is not shown and the faint-sample conclusion is indirect. read the letter →

arxiv 1908.11448 v4 pith:QAKWLHGG submitted 2019-08-29 astro-ph.CO astro-ph.GA

Gillian D. Beltz-Mohrmann , Andreas A. Berlind , Adam O. Szewciw This is my paper · ORCID
classification astro-ph.COastro-ph.GA
keywords halooccupationdistributiongalaxyclusteringhydrodynamicsimulationsmassfunctionassemblybiassatellitespatialvelocitycounts-in-cellsstatistics
topics Dark Matter
open problems Dark Matter
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 asks whether the standard five-parameter halo occupation distribution (HOD) — the usual recipe for placing galaxies inside dark matter haloes — can reproduce the galaxy clustering of full hydrodynamic simulations. The answer it argues is yes for bright galaxies, and only with extra parameters for faint ones. Baryonic feedback shifts the halo mass function to lower masses, so applying an HOD calibrated on a hydrodynamic run to a dark-matter-only run produces too many galaxies. Once the dark-matter-only halo masses are rank-matched to undo that shift, the five-parameter HOD reproduces every clustering statistic tested for the bright sample in both simulations. The faint sample requires additional spatial, velocity, and assembly-bias freedom; the paper shows that removing those biases from the simulation one by one restores agreement.

What carries the argument

The engine is the "vanilla" HOD: central galaxies are placed with probability $\langle N_{\mathrm{cen}}\rangle = \frac{1}{2}[1+\mathrm{erf}((\log M-\log M_{\min})/\sigma_{\log M})]$, and satellites are Poisson draws with mean $\langle N_{\mathrm{sat}}\rangle = \langle N_{\mathrm{cen}}\rangle((M-M_0)/M_1)^\alpha$. The second piece is a rank-based mass correction: dark-matter-only haloes are sorted by mass and assigned the mass of the hydrodynamic halo at the same rank, giving each dark-matter-only halo a multiplier that recovers the hydrodynamic halo mass function. The third piece is a diagnostic protocol: replacing satellites' positions and velocities with random dark-matter particle values removes spatial and velocity bias, while swapping galaxies between haloes of similar mass removes assembly bias; the improvement in agreement after each operation identifies which missing ingredient the baseline model needs.

What would settle it

Compare the rank-based mass ratios shown in Figure 8 with ratios obtained by matching haloes between the hydrodynamic and dark-matter-only runs through their particle IDs; if the two mass-ratio curves disagree, the correction is not isolating a pure baryonic mass shift, and the reported clustering agreement could be a coincidence. A second check is to recompute the correction separately in high- and low-density regions and see whether a single multiplier fits both.

Watch

Extended reading notes

Core claim

The paper's central claim is that the standard five-parameter HOD is not inherently inadequate, but it is usually applied to the wrong haloes. In the hydrodynamic runs, baryonic feedback lowers halo masses relative to the dark-matter-only runs, shifting the halo mass function to lower masses, so the same best-fitting HOD populates too many high-mass haloes and overproduces galaxies. The paper corrects this by rank-matching dark-matter-only haloes to hydrodynamic haloes and multiplying each mass by the ratio of the two, which makes the mass functions agree. After that correction, the five-parameter HOD reproduces the projected correlation function, the redshift-space correlation function, the group multiplicity function, the void probability function, the singular probability function, and the number density for the bright galaxy sample in both simulations. The faint sample does not agree on most of these statistics until satellite spatial bias, satellite and central velocity bias, and assembly bias are successively removed from the simulation galaxies; the paper reads this as evidence that faint samples need HOD parameters for those biases, while bright samples do not. The exact baryonic correction is simulation-dependent, which the authors take as a warning that any fixed correction carries systematic uncertainty.

Load-bearing premise

The whole post-correction result rests on assuming that matching dark-matter-only haloes to hydrodynamic haloes by mass rank pairs the same halo population, so the correction only shifts halo masses and does not accidentally erase environmental or clustering information; if that pairing is wrong, the bright-sample agreement could be an artifact.

Editorial extensions

If this is right

  • Bright galaxy samples can be modelled with the standard five-parameter HOD, provided the dark-matter-only halo mass function is first corrected for the baryonic shift.
  • Faint galaxy samples will require extended HODs that include spatial, velocity, and assembly-bias parameters; vanilla HOD fits to faint samples will inherit systematic bias.
  • Galaxy number density is a sharp diagnostic: a dark-matter-only HOD run that matches correlation functions but overproduces number density is probably missing the baryonic halo-mass correction.
  • Because the baryonic correction differs between the two simulations, HOD analyses of real surveys should repeat with several plausible corrections to quantify the systematic uncertainty.
  • The void probability function is especially sensitive to assembly bias, so surveys should measure counts-in-cells statistics in addition to correlation functions when constraining extended HOD parameters.

Reading between the lines

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

  • A direct test of the correction is to run the same rank-matching on a third hydrodynamic simulation with different feedback physics; the spread in the required mass-ratio curves would show how much of the bright-sample success is simulation-specific.
  • The bias-removal protocol could be inverted into a calibration: inject known spatial, velocity, and assembly-bias amplitudes into dark-matter-only mocks and check whether the proposed HOD extensions recover the injected values.
  • The rank-based correction assumes a single global mass shift, so it likely misses environment-dependent baryonic effects at low masses; a natural extension is a correction that also depends on halo concentration or local density.
  • The paper's division between bright and faint samples suggests that cosmological constraints from bright galaxy clustering are less affected by uncertain baryonic feedback, so future surveys may want to prioritize bright samples for HOD-based cosmology.
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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

2 major / 4 minor

Summary. The paper tests whether the standard five-parameter HOD of Zheng et al. (2007) can reproduce galaxy clustering in two hydrodynamic simulations, Illustris-2 and EAGLE, for a high- and a low-luminosity threshold sample. For each simulation and sample, the HOD parameters are fitted to the mean central and satellite occupation functions of the hydrodynamic run, and the same parameters are then applied to the DMO counterpart simulation to generate 1000 mock catalogues. Six statistics are measured on both the hydrodynamic galaxies and the mocks: galaxy number density, the projected and redshift-space two-point correlation functions, the group multiplicity function, the void probability function, and a 'singular probability function.' The authors find that the HOD systematically overpredicts the number density in every case, which they trace to baryons shifting the halo mass function to lower masses in both simulations, albeit with different mass dependence (Section 6). After correcting the DMO halo masses by rank-based abundance matching to the hydrodynamic haloes, the vanilla HOD reproduces all clustering statistics for the high-luminosity samples at roughly the 2-3 sigma level.

Significance. If the central high-luminosity result holds, the paper is a useful quantitative demonstration of a systematic that is usually ignored in HOD applications: baryonic feedback shifts the halo mass function in a simulation-dependent way, and the correction must be calibrated rather than assumed. The study has notable strengths. The HOD is fitted only to the occupation function, so the projected and redshift-space correlation functions, group multiplicity function, VPF, and SPF are out-of-sample predictions; the number density, by contrast, is essentially fixed by the HMF correction and the HOD fit, a point the paper should state explicitly. The use of two independent hydrodynamic codes with different numerics and feedback models gives some handle on theoretical systematics, and the suite of six statistics, including the rarely used VPF and SPF, provides diagnostic power beyond the usual two-point clustering. The paper also provides fitting functions for the baryonic mass correction (Table 4) that are directly useful to the community.

major comments (2)
  1. [Section 6, Figures 7–9] The abstract's high-luminosity claim ('After applying a correction to the halo mass function in each simulation, the HOD is able to accurately reproduce all clustering statistics') rests entirely on the rank-based abundance-matching correction of DMO halo masses (Section 6, Figure 8). That correction is only valid if the baryonic mass shift is essentially independent of environment; the manuscript says 'We have examined the conditional HMF in Illustris ... the effect of baryons on the HMF only depends on environment at very high halo masses' and that an environment-dependent correction changes the clustering statistics 'negligibly,' but no such analysis is shown, and no analogous check is reported for EAGLE. Because the correction makes the global HMF (and, together with the HOD fit to the occupation function, the galaxy number density) agree by construction, the nontrivial content of the high-luminosity claim is the spatial and velocity clustering of the corrected halo population. If the rank mapping assigns systematically wrong masses to DMO haloes in particular environments, the agreement in wp(rp) and xi(s) could be an artifact of the correction method rather than evidence for the HOD. I request that the authors (i) show the conditional mass ratio M_hydro/M_DMO in environment bins for both simulations, (ii) repeat the clustering comparison using an alternative correction, e.g., position- or particle-ID-matched haloes or an environment-dependent correction, and (iii) present the halo correlation function comparison that is currently described only in words in Section 6.
  2. [Section 7, Table 3] The low-luminosity conclusion is established by removing effects from the hydrodynamic simulation galaxies rather than by fitting an extended HOD. The abstract's wording ('we find evidence that ... is necessary') is appropriately hedged, but the conclusions should state explicitly that the removal experiments test necessity, not sufficiency: they show that a vanilla HOD cannot match galaxies that exhibit spatial/velocity/assembly bias, but they do not demonstrate that an HOD with free bias parameters can fit the original simulation statistics. In addition, the assembly-bias removal procedure (Section 7.3) swaps galaxies between 'pairs of haloes with similar masses' without specifying the mass tolerance or the construction of the four pairings used to generate the 4000 realizations; the reported p-values could depend on these choices. Please specify the pairing criterion and test sensitivity to it. A direct check of whether a decorated HOD (e.g., Hearin et al. 2016) with bias parameters can reproduce the low-luminosity clustering would considerably strengthen the paper's central recommendation.
minor comments (4)
  1. [Section 6] The statement that for the M−21r samples 'all clustering statistics are at or better than the 2σ level' after the HMF correction is not consistent with Table 3 for EAGLE: wp(rp) has p=3.64×10^-2 and xi(s) has p=4.07×10^-2, below the conventional two-sided 2σ threshold (p≈0.0455). Please state the σ convention used or reword the claim.
  2. [Section 6] The post-correction number density agreement is close to guaranteed: both the HOD parameters (Section 3.2) and the HMF correction (Section 6) are derived from the same hydrodynamic simulation, so the number-density p-values after correction are a consistency check rather than an independent prediction. The paper should say this when presenting the corrected number-density p-values.
  3. [Section 8] The bullet list in the summary contains a grammatical error: 'It also able to accurately reproduce galaxy number density' should read 'It is also able to ...'.
  4. [Figure 9 caption] The caption says 'The values of these points are given in Tables 3'; this should be 'Table 3'.

Circularity Check

1 steps flagged · score 4.0 of 10

High-luminosity success is partly circular: the HMF correction is built from the same simulations, so the corrected number-density agreement is forced; the other clustering statistics are genuinely out-of-sample and unsullied.

  1. fitted input called prediction [Section 6 ('The Effect of Baryons on the Halo Mass Function'), Figure 8 procedure and Table 3 rows labeled 'Halo Mass Function']
    "We do this by identifying the most massive halo in the dark matter only simulation and assigning it the mass of the most massive halo in the hydrodynamic version, and then we do the same for the next most massive halo, and so on. In other words, we multiply the DMO halo masses in each simulation by their y-axis value in Figure 8. This process serves to isolate the effect of baryons on the halo mass function, allowing us to correct the DMO HMFs so that they agree with the HMFs from the hydrodynamic simulations."

    The correction factor is computed from the same hydrodynamic and DMO simulations that define the comparison target, and the procedure explicitly forces the corrected DMO halo mass function to equal the hydrodynamic HMF. The HOD parameters were themselves fit to the hydrodynamic galaxy occupation in Section 3.2. Therefore the post-correction galaxy number density is not an out-of-sample prediction: ng = ∫(dN_DMO,corrected/dM)<N_fit(M)>dM equals ∫(dN_hydro/dM)<N_hydro(M)>dM by construction, up to the quality of the occupation fit. The high p-values for number density in the 'Halo Mass Function' rows of Table 3 therefore largely reflect the in-sample HOD fit, not a successful prediction.

full rationale

The paper's central derivation is mostly self-contained and the clustering comparisons are legitimate: five-parameter HODs are fit to hydrodynamic galaxy occupations, applied to DMO haloes, and six clustering statistics are measured in matched ways. The main circular element is the halo-mass-function correction. The rank-based abundance-matching ratio in Figure 8 is derived from the same two simulations that serve as the target, and the paper explicitly uses it to force the DMO HMF to agree with the hydrodynamic HMF. Because the HOD was already fit to those same hydrodynamic galaxies, the corrected number density is a fitted input renamed as a successful prediction, not an independent test. This affects only the number-density component of the 'all clustering statistics' claim; the other five statistics are not used in the fits, and the persistent low-luminosity discrepancies are nontrivial. There is no load-bearing self-citation chain, no imported uniqueness theorem, and no ansatz smuggled in via citation. The rank-matching method's environmental robustness is a correctness risk rather than a circularity, since the paper reports but does not show those checks. Overall the central claim is partially constructed from its inputs but retains substantial independent content, giving a score of 4.

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

The central HOD parameters are five fitted parameters per sample. The analysis additionally depends on the validity of the hydrodynamic simulations as truth, the vanilla HOD's mass-only and Poisson assumptions, the rank-based HMF correction, and the bias-removal swapping procedure. No new physical entities are introduced.

free parameters (5)
  • HOD log M_min = Illustris -21/-19, EAGLE -21/-19: 12.681, 11.500, 12.767, 11.555
    Mass at which half of haloes host a central galaxy; fit to each simulation and luminosity sample.
  • HOD sigma_logM = 0.532, 0.180, 0.504, 0.237
    Scatter in halo mass for central occupation; fit to occupation data.
  • HOD log M_0 = 12.296, 11.659, 12.467, 11.717
    Halo mass below which no satellites are placed; fit parameter.
  • HOD log M_1 = 13.635, 12.590, 13.799, 12.566
    Halo mass with one satellite galaxy on average; fit parameter.
  • HOD alpha = 0.994, 0.979, 1.000, 0.938
    Slope of the satellite occupation power law at high mass; fit parameter.
assumptions (5)
  • domain assumption Illustris-2 and EAGLE hydrodynamic simulations are adequate stand-ins for real galaxy formation when testing the HOD framework.
    All comparisons treat the simulation galaxies as truth; the authors explicitly note there is no consensus among hydrodynamic simulations (Section 8).
  • domain assumption In the vanilla HOD, mean occupation depends only on halo mass, with central and satellite components given by Eqs. (1) and (2).
    This is the modelling assumption under test; it is used to fit and apply the HOD.
  • domain assumption Satellite galaxy counts are Poisson and satellite positions and velocities trace dark matter particles, while centrals sit at halo centers.
    Section 3.1; the paper later tests deviations from these assumptions.
  • domain assumption Rank-based abundance matching of DMO halo masses to hydro halo masses yields the correct baryonic halo mass correction.
    Section 6; if rank matching does not preserve the correct halo population, the post-correction clustering agreement would be an artifact.
  • domain assumption The galaxy-swapping procedure in Section 7.3 removes assembly bias without otherwise changing the clustering signal.
    The conclusion that assembly bias parameters are needed relies on this procedure preserving everything except occupation dependence on secondary halo properties.

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Cite this review

Pith. "Pith review of Testing the Accuracy of Halo Occupation Distribution Modelling using Hydrodynamic Simulations." pith.science (2026). https://pith.science/paper/QAKWLHGG

@misc{pith2026190811448,
  author       = {Pith},
  title        = {Pith review of: Testing the Accuracy of Halo Occupation Distribution Modelling using Hydrodynamic Simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QAKWLHGG}},
  note         = {Machine review of arXiv:1908.11448}
}
read the original abstract

Halo models provide a simple and computationally inexpensive way to investigate the connection between galaxies and their dark matter haloes. However, these models rely on the assumption that the role of baryons can be easily parametrized in the modelling procedure. We aim to examine the ability of halo occupation distribution (HOD) modelling to reproduce the galaxy clustering found in two different hydrodynamic simulations, Illustris and EAGLE. For each simulation, we measure several galaxy clustering statistics on two different luminosity threshold samples. We then apply a simple five parameter HOD, which was fit to each simulation separately, to the corresponding dark matter only simulations, and measure the same clustering statistics. We find that the halo mass function is shifted to lower masses in the hydrodynamic simulations, resulting in a galaxy number density that is too high when an HOD is applied to the dark matter only simulation. However, the exact way in which baryons alter the mass function is remarkably different in the two simulations. After applying a correction to the halo mass function in each simulation, the HOD is able to accurately reproduce all clustering statistics for the high luminosity sample of galaxies. For the low luminosity sample, we find evidence that in addition to correcting the halo mass function, including spatial, velocity, and assembly bias parameters in the HOD is necessary to accurately reproduce clustering statistics.

Figures

Figures reproduced from arXiv: 1908.11448 by the authors.

Figure 1
Figure 1. Best-fitting HOD for Illustris-2 (left) and EAGLE (right) galaxies. The Illustris-2 high luminosity (M−21 r ) galaxy sample is plotted with a solid red line, and the low luminosity (M−19 r ) sample is plotted with a dashed red line, while the EAGLE high luminosity sample is plotted with a solid blue line, and the low luminosity sample is plotted with a dashed blue line. The gray lines in each case show 300 realizati… view at source ↗
Figure 2
Figure 2. The second moment of the HOD for Illustris-2 M−19 r galaxies (red points, left) and EAGLE M−19 r galaxies (blue points, right). The dark and light gray shaded regions show the inner 68 and 95% of the realizations of the best-fitting HOD model for that sample, and the black points are the median of the 300 realizations. vestigate this assumption we examine the average number of satellite-satellite pairs per halo in b… view at source ↗
Figure 3
Figure 3. All clustering measurements for the M−21 r sample of Illustris-2 galaxies. The red lines are measured on galaxies from the original hydrodynamic simulation, while the dark red lines show the average of 1000 realizations of the best-fitting HOD model applied to the dark matter only simulation. The error bars represent the standard deviation among the 1000 realizations. The shaded regions around the red lines show cos… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Same as [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 8
Figure 8. Figure 8: emphasizes the fact that the effect of baryons on the halo mass function is to decrease the HMF to lower masses. However, it is clear that this effect is very different in these two different simulations. The effect of baryons on the [PITH_FULL_IMAGE:figures/full_fig_…
Figure 9
Figure 9. Figure 9: p-values from comparing the clustering of galaxies in hydrodynamic simulations to the clustering of mock galaxies in their dark matter only (DMO) counterparts. Each panel shows results for a different clustering statistic, as listed at the top of each panel. The dark r…

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    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.