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REVIEW 3 major objections 5 minor 88 references

Tomographic halo model of the unWISE-Blue galaxies using cross-correlations with BOSS CMASS galaxies

T0 review · 3 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read A new cross-correlation method measures how unWISE-Blue galaxy halos evolve with redshift, finding lower bias, lower mean halo mass, and fewer satellite galaxies at higher redshift.

desk verdict Solid tomographic HOD work whose central unWISE-Blue evolution result is conditional on an untested occupation-correlation assumption; worth refereeing, not desk-rejecting. read the letter →

arxiv 2502.02744 v2 pith:ZT4WBI3P submitted 2025-02-04 astro-ph.CO astro-ph.GA

Alex Krolewski , Jensen Lawrence , Will J. Percival This is my paper · ORCID
classification astro-ph.COastro-ph.GA
keywords halooccupationdistributiongalaxyclusteringcross-correlationphotometricredshiftsunWISEBOSSCMASStomographicanalysismodel
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 develops a halo-model framework for cross-correlating a photometric galaxy sample with a broad, poorly resolved redshift distribution against a spectroscopic sample split into narrow redshift bins, and applies it to the unWISE-Blue sample and the BOSS CMASS sample. It measures how the halo occupation of unWISE-Blue galaxies changes between $z = 0.45$ and $0.75$: average bias falls from about $1.6$ at $z \sim 0.5$ to about $1.4$ at $z \sim 0.7$, mean halo mass falls from about $10^{13.4}$ to $10^{13.1}$ solar masses, and the satellite fraction drops from roughly $20\%$ to $10\%$. These constraints are directly usable for building mock catalogs of unWISE-Blue and for interpreting cross-correlations of the sample with other surveys, since unWISE-Blue cannot be split photometrically by redshift.

What carries the argument

The load-bearing object is the halo occupation distribution (HOD), the mean number of central and satellite galaxies in a dark-matter halo of mass $M$, parametrized by $M_{\min}$, $M_1$, $M_0$, $\alpha$, and $\sigma_{\log M}$. The paper extends this HOD to the cross-correlation of two tracer populations by adding occupation correlation coefficients $R_{\mathrm{cs}}$, $R_{\mathrm{ss}}$, and $R_{\mathrm{sc}}$ between the two samples' centrals and satellites, here fixed to zero. Geometrically, the method replaces the Limber approximation with a post-Limber integral suited to narrow spectroscopic bins, adds linear redshift-space distortions, incorporates halo exclusion so that overlapping halos are not counted twice, and adds a lensing-magnification term evaluated at the halo model's linear bias. These pieces let the model predict the angular cross-correlation of a broad photometric sample with a narrow spectroscopic bin at scales from $0.1$ to $10\,h^{-1}\,\mathrm{Mpc}$.

What would settle it

Measure the clustering of the two populations inside the same halos, for example using a group or cluster catalog to compare the fraction of CMASS host halos that also contain unWISE-Blue galaxies with the uncorrelated-model prediction. If allowing the occupation correlation coefficients to be nonzero moves the inferred unWISE-Blue bias or mean halo mass by more than the quoted errors in any redshift bin, the central trend would not hold.

Watch

Extended reading notes

Core claim

The central claim is that a redshift-independent halo occupation distribution cannot describe unWISE-Blue galaxies; their HOD evolves modestly but detectably across $0.45 < z < 0.75$. In the baseline model, the mean halo mass falls from $\log_{10}(M_{\mathrm{h}}/M_\odot) \sim 13.4$ to $\sim 13.1$ and the linear bias from $\sim 1.6$ to $\sim 1.4$ between $z \sim 0.5$ and $z \sim 0.7$, with the satellite fraction declining from $\sim 20\%$ to $\sim 10\%$. The same analysis finds strong evolution in the CMASS HOD, with $M_{\min}$ increasing from $\log_{10}(M_{\min}/M_\odot) \sim 13.28$ to $\sim 14.67$ while the mean halo mass stays near $\log_{10}(M_{\mathrm{h}}/M_\odot) \sim 13.55$ because the evolving halo mass function cancels the HOD shift. The enabling discovery is the method itself: a halo model for photometric-spectroscopic cross-correlations that includes post-Limber corrections, redshift-space distortions, halo exclusion, and lensing magnification, and fits both the CMASS autocorrelation and the CMASS-unWISE cross-correlation from $0.1$ to $10\,h^{-1}\,\mathrm{Mpc}$.

Load-bearing premise

The analysis assumes that CMASS and unWISE-Blue galaxies occupy dark-matter halos independently, so that the correlation coefficients $R_{\mathrm{cs}}$, $R_{\mathrm{ss}}$, and $R_{\mathrm{sc}}$ between their central and satellite occupations, fixed to zero, do not bias the inferred halo masses.

Editorial extensions

If this is right

  • If the central claim holds, mock catalogs of unWISE-Blue should assign galaxies to halos using an HOD that changes across $0.45 < z < 0.75$, not a single redshift-independent occupation.
  • Any single-number summary of unWISE-Blue clustering, such as one bias value or one mean halo mass, is a redshift-averaged quantity that hides the measured decline in halo mass and satellite fraction.
  • The same post-Limber, RSD-inclusive halo model should apply to other photometric-spectroscopic cross-correlation pairs, including clustering-redshift measurements where narrow spectroscopic bins make the Limber approximation inadequate.
  • For CMASS, the near-constant mean halo mass combined with strongly changing $M_{\min}$ and $\sigma_{\log M}$ shows that redshift evolution in the HOD can be masked by the evolving halo mass function, so number-density evolution alone would be a misleading proxy.

Reading between the lines

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

  • If the occupation independence assumption were relaxed, allowing CMASS and unWISE-Blue galaxies to prefer or avoid sharing halos, the inferred unWISE-Blue halo masses could shift and the apparent decline with redshift could shrink or steepen.
  • The unWISE-Blue color selection itself may track a stellar-mass range that evolves with redshift, so part of the measured drop in halo mass could be a selection effect rather than a change in host halos; cross-correlating with a lower-redshift spectroscopic sample would test whether the decline continues below $z = 0.45$.
  • Because the method needs only a broad photometric kernel, it offers a route to measure HODs for other all-sky photometric samples that lack accurate photometric redshifts, effectively turning a spectroscopic tracer into a tomographic probe.
  • The strong degeneracy between $M_{\min}$ and $\sigma_{\log M}$ suggests that the individually reported parameters are less secure than the derived combinations such as bias and mean halo mass, which are the quantities that drive the paper's main conclusion.
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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 / 5 minor

Summary. The paper develops a tomographic halo-model analysis of the unWISE-Blue galaxy sample using its cross-correlation with BOSS CMASS galaxies in six narrow redshift bins between z=0.45 and z=0.75. The authors extend the HALOMOD code to include post-Limber corrections, redshift-space distortions, halo exclusion, and magnification bias, and jointly fit CMASS autocorrelations and CMASS-unWISE cross-correlations with a 10-parameter HOD model. They report that the CMASS HOD evolves strongly with redshift while the unWISE-Blue HOD evolves modestly, with mean bias and halo mass decreasing from b~1.6 and log M_h~13.4 at z~0.5 to b~1.4 and log M_h~13.1 at z~0.7, and satellite fraction dropping from ~20% to ~10%. The method is presented as a general tool for tomographic cross-correlation HOD fitting.

Significance. If the results hold, this is a useful methodological advance: it demonstrates that photometric-spectroscopic cross-correlations can be used to infer redshift-resolved HODs for broad-redshift photometric samples, with direct applications to clustering redshifts and mock catalog construction. The paper is careful in treating many observational systematics (fiber collisions, imaging systematics, magnification, integral constraint), and it releases publicly available fitting code. The unWISE-Blue HOD constraints, if robust, would improve understanding of an important all-sky infrared-selected sample and inform its use in CMB lensing and other cross-correlation analyses. The fit quality is good, with chi-square per degree of freedom between 0.6 and 1.8 across redshift bins.

major comments (3)
  1. [Section 4.2, Eq. (26)] Section 4.2, Eq. (26): The cross-correlation occupation coefficients Rcs, Rss, and Rsc are fixed to zero, which is the uncorrelated-occupation assumption. This assumption directly enters the 1-halo cross-power spectrum P12^1h(k) in Eq. (26), where the mixed moments such as <Nc,1 Ns,2> factorize only under this assumption. Because CMASS and unWISE-Blue occupy halos of similar mass (mean halo masses ~13.55 and ~13.3 in Tables 2 and 3), correlated occupation is physically plausible, and nonzero values of these coefficients would change the small-scale cross-correlation amplitude. Since the paper does not include an unWISE autocorrelation measurement, the cross-correlation data alone cannot break the degeneracy between the unWISE satellite HOD parameters and the occupation-correlation coefficients. The paper explicitly leaves this to future work, but the claimed redshift evolution of the unWISE-Blue HOD (Section 5.2.1) is the central science result and depends on this untested assumption. I request that the authors quantify the impact, for example by repeating the fits with Rcs/Rss/Rsc set to extreme values (e.g., +1, -1) or by marginalizing over them with reasonable priors, and report how the derived bias, mean halo mass, and satellite fraction shift.
  2. [Section 2.1, Eq. (38)] The unWISE-Blue redshift distribution n(z) is measured from the COSMOS2015 catalog in the 2 deg^2 COSMOS field and assumed to be representative of the full sky. This n(z) enters the likelihood through the number-density constraint in Eq. (38) and through the projection of the model correlation function. The paper accounts only for Poisson fluctuations in the COSMOS counts (Fig. 1), but not for cosmic variance or field-to-field variations, which are known to be significant for a 2 deg^2 field at z~0.5. A biased n(z) would directly shift the inferred HOD parameters, especially Mmin and sigma_logM, and could thereby contaminate the claimed redshift evolution of the unWISE-Blue HOD. Please estimate the cosmic-variance contribution to sigma_nbar, or test robustness by adopting alternative n(z) priors or by marginalizing over the n(z) shape within a broader family of distributions.
  3. [Section 5.2.1, Table 3] The abstract states that the unWISE-Blue bias and mean halo mass 'drop' from b~1.6 and log M_h~13.4 at z~0.5 to b~1.4 and log M_h~13.1 at z~0.7, but the measured derived parameters in Table 3 are non-monotonic: the bias is 1.53, 1.63, 1.48, 1.37, 1.43, 1.64 in the six bins, and the mean halo mass is 13.40, 13.43, 13.29, 13.14, 13.11, 13.20. The final bin is consistent with the first two bins in bias, and the apparent decline is driven by the middle bins. The paper states that the best-fit HOD in any bin is strongly ruled out in other bins, but this claim is not shown quantitatively. Please provide a significance test for the redshift evolution of the derived parameters (e.g., chi-square of a constant-bias or constant-mass model against the six measurements, accounting for correlations between bins if available), and adjust the abstract and conclusions so that the characterization of the evolution matches the actual trend in the data.
minor comments (5)
  1. [Section 4.3.5] Typo: 'magnificantion' should be 'magnification' in the sentence introducing the binned model.
  2. [Fig. 9 caption] Typo: 'occurr' should be 'occur' in the caption.
  3. [Section 1] Typo: 'background' is misspelled as 'backgpround' in the sentence about the cosmic infrared background.
  4. [Section 3] The Davis-Peebles estimator in Eq. (2) is used instead of Landy-Szalay because of the computational cost of the RR term for the dense unWISE sample; the paper does not discuss the well-known bias of the Davis-Peebles estimator on small scales. A short justification or a reference demonstrating that this bias is negligible for the scales and densities here would be helpful.
  5. [Section 4.3.4] The notation in Eq. (30) for the magnification contributions (w_mu1_g2, w_g1_mu2, w_mu1_mu2) is clear, but the text immediately after uses 'w_g_mu' and 'w_mu1_mu2' without explicitly connecting these to the three terms in Eq. (30). A consistent labelling would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the HOD parameters are fitted to the clustering data, and the quoted bias, mean halo mass, and satellite fraction are transformations of those fits, not independent predictions; the external inputs are independent measurements, and no step reduces a claimed result to its own input by construction.

full rationale

The derivation chain is a standard likelihood fit: the ten HOD parameters (five for CMASS, five for unWISE-Blue) are adjusted to reproduce the joint data vector of CMASS autocorrelations and CMASS-unWISE cross-correlations, with Gaussian or step-function number-density constraints. The headline quantities (bias, mean halo mass, satellite fraction) are computed from the fitted occupation functions via the halo-model integrals; they are reparameterizations of the fit rather than a priori predictions, but the paper consistently presents them as measurements ('we find') and does not mislabel them as independent predictions. The fixed-zero occupation correlations Rcs/Rss/Rsc in Section 4.2 and Eq. 26 are an acknowledged modeling assumption that could bias the inferred unWISE-Blue HOD and its redshift evolution, but this is a systematic or model-degeneracy concern, not circularity: the paper does not define the target quantities in terms of these coefficients, and it explicitly flags the impact as future work. The unWISE redshift distribution and magnification slope s are taken from Krolewski et al. (2020), and the CMASS magnification slopes from Farren et al. (2024); these are independent, externally measurable inputs (COSMOS photometric redshifts and the response of number counts to photometric perturbations), not consequences of the target HOD. Footnote 8 correctly states that predicting the unWISE autocorrelation or CMB-lensing cross-correlation would require HOD constraints outside the fitted redshift range; that is a stated limitation, not a circular step. No equation reduces a claimed result to a fitted parameter renamed as a prediction, and no load-bearing conclusion is imported solely through a self-citation.

Assumptions & free parameters 11 free parameters · 6 assumptions · 0 invented entities

The HOD parameters are fitted to the clustering data rather than predicted, and the central 'evolution' results are transformations of these fits. Several strong domain assumptions are imported from prior literature, and two paper-specific assumptions (independent occupations and representative COSMOS n(z)) are untested.

free parameters (11)
  • CMASS Mmin = 13.28 to 14.69 across bins
    Central galaxy threshold mass, fitted in each redshift bin (Table 2).
  • CMASS M1 = 14.03 to 14.54
    Satellite mass scale, fitted in each redshift bin (Table 2).
  • CMASS alpha = 0.77 to 1.50
    Satellite power-law slope, fitted in each redshift bin (Table 2).
  • CMASS M0 = 12.5 to 13.7
    Satellite cutoff mass, fitted in each redshift bin (Table 2).
  • CMASS sigma_logM = 0.67 to 1.13
    Central cutoff width, fitted in each redshift bin (Table 2).
  • unWISE-Blue Mmin = 12.20 to 12.99 (default case)
    Central galaxy threshold mass, fitted in each redshift bin (Table 3).
  • unWISE-Blue M1 = 13.16 to 13.50
    Satellite mass scale, fitted in each redshift bin (Table 3).
  • unWISE-Blue alpha = 0.89 to 1.30
    Satellite power-law slope, fitted in each redshift bin (Table 3).
  • unWISE-Blue M0 = 12.2 to 13.0
    Satellite cutoff mass, fitted in each redshift bin (Table 3).
  • unWISE-Blue sigma_logM = 0.22 to 1.15
    Central cutoff width, fitted in each redshift bin (Table 3).
  • unWISE-Blue finc = 0.48 to 0.95 (incompleteness case)
    Asymptotic high-mass completeness, fitted in the alternative model (Table 5).
assumptions (6)
  • domain assumption Zheng et al. (2007) HOD functional form with erf central and power-law satellite terms
    Assumed model for N(M), Section 4.2; results depend on this functional form.
  • domain assumption Halo model ingredients: NFW profile, Tinker mass function and bias, Duffy concentration-mass relation, Planck 2015 cosmology
    Standard inputs from prior literature, Section 4.1; not fitted in this work.
  • standard math Simon (2007) post-Limber approximation for narrow redshift bins
    Used to compute the angular correlation function in Equation 15; assumed valid for the narrow bins and scales considered.
  • standard math Kaiser (1987) linear redshift-space distortion model
    RSD treatment in Equation 18; assumes linear regime, with small expected impact on angular clustering.
  • ad hoc to paper Cross-correlation occupation coefficients Rcs=Rss=Rsc=0
    Independent occupation assumption in Section 4.2; untested and potentially biasing the inferred HOD.
  • ad hoc to paper unWISE-Blue redshift distribution from COSMOS2015 is representative of the full sky
    Used as the photometric redshift kernel in Section 2.1; uncertainty is not propagated into the HOD constraints.

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Cite this review

Pith. "Pith review of Tomographic halo model of the unWISE-Blue galaxies using cross-correlations with BOSS CMASS galaxies." pith.science (2026). https://pith.science/paper/ZT4WBI3P

@misc{pith2026250202744,
  author       = {Pith},
  title        = {Pith review of: Tomographic halo model of the unWISE-Blue galaxies using cross-correlations with BOSS CMASS galaxies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZT4WBI3P}},
  note         = {Machine review of arXiv:2502.02744}
}
abstract

The halo model offers a framework for investigating galaxy clustering, and for understanding the growth of galaxies and the distribution of galaxies of different types. Here, we use the halo model to study the small-scale clustering and halo occupation distribution (HOD) of the unWISE-Blue galaxy sample, an infrared-selected sample of $\sim$100 million galaxies across the entire extragalactic sky at $z\sim 0.5$ $-$ similar redshifts to the Baryon Oscillation Spectroscopic Survey (BOSS) CMASS sample. Although the photometric unWISE galaxies cannot be easily split in redshift, we use their cross-correlation with the BOSS CMASS sample to tomographically probe the HOD of the unWISE galaxies at $0.45 < z < 0.75$. To do so, we develop a new method for applying the halo model to cross-correlations between a photometric sample and a spectroscopic sample in narrow redshift bins, incorporating halo exclusion, post-Limber corrections, and redshift-space distortions. We reveal strong evolution in the CMASS HOD, and modest evolution in the unWISE-Blue HOD. For unWISE-Blue, we find that the average bias and mean halo mass drop from $b = 1.6$ and $\log_{10}(M_{\mathrm{h}}/M_{\odot}) \sim 13.4$ at $z \sim 0.5$ to $b = 1.4$ and $\log_{10}(M_{\mathrm{h}}/M_{\odot}) \sim 13.1$ at $z \sim 0.7$, and that the satellite fraction drops modestly from $\sim$20% to $\sim$10% in the same range. These results are useful for creating mock samples of the unWISE-Blue galaxies. Furthermore, the techniques developed to obtain these results are applicable to other tomographic cross-correlations between photometric samples and narrowly-binned spectroscopic samples, such as clustering redshifts.

Figures

Figures reproduced from arXiv: 2502.02744 by the authors.

Figure 1
Figure 1. — Number densities of unWISE-Blue (blue) and CMASS (orange) galaxy samples. The gray shaded regions demarcate the different redshift bins. Uncertainties on the unWISE-Blue ¯n(z) are from Poisson fluctuations in the observed photo-z number counts in the 2 deg2 COSMOS field. offset to the CMASS galaxies’ flux across all bands,3 and also account for the change in redshift success rate as the galaxies get brighter from … view at source ↗
Figure 2
Figure 2. — The jackknife correlation matrix for the 0.5 < z < 0.55 redshift bin, with axes labelled by bin number. The black dotted lines separate the matrix into its component blocks: the upper left block is the CMASS autocorrelation matrix while the lower right block is the CMASS-unWISE cross-correlation matrix. The autocorrelation matrix has fewer elements due to the small-scale cut removing scales affected by fiber colli… view at source ↗
Figure 3
Figure 3. — The angular correlation function data and best-fit models for the CMASS autocorrelation (left column) and the CMASS-unWISE cross-correlation (right column) in the redshift bins 0.5 < z < 0.55 (top row) and 0.7 < z < 0.75 (bottom row), with jackknife errors as described in Section 3. The Base best-fit considers only the standard Limber approximation to w(θ). In contrast, the PL best-fit uses the post-Limber equatio… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: — The angular correlation function data and overall best-fit models for the CMASS autocorrelation (left column) and the CMASS￾unWISE cross-correlation (right column). From top to bottom, the rows correspond to the redshift bins 0.45 < z < 0.5, 0.5 < z < 0.55, 0.55 < z …
Figure 5
Figure 5. Figure 5: — Evolution of the 5 HOD parameters for the CMASS (left column) and unWISE-Blue (right column) galaxies as a function of redshift. The unWISE-Blue panels show both the default case where we use the observed ¯n in the likelihood, and the “incompleteness” case where the …
Figure 6
Figure 6. Figure 6: — Evolution of the derived bias, mean halo mass (M¯ h), and satellite fraction (fsat), parameters for the CMASS (left column) and unWISE-Blue (right column) galaxies as a function of redshift. The unWISE-Blue panels show both the default case where we use the observed …
Figure 7
Figure 7. Figure 7: — [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: — Comparison between our best-fit ⟨N(m)⟩ to the CMASS galaxies (gray lines) and those of Saito et al. (2016) (S2016; green lines). The solid lines depict ⟨Nc(m)⟩ while the dashed lines depict ⟨Ns(m)⟩. The S2016 measurements are reported in different redshift bins from …
Figure 9
Figure 9. Figure 9: — The mean number of central galaxies (top row) and the mean number of satellite galaxies (bottom row) for the unWISE-Blue HOD as functions of halo mass. The left column corresponds to the default case where we use the observed value of ¯n, while the right column corre…
Figure 10
Figure 10. Figure 10: — Constraints and degeneracies between the 10 HOD parameters at 0.55 < z < 0.6. A subscript C denotes the CMASS HOD parameters while a subscript W denotes the unWISE-Blue HOD parameters. The default model is in red, and the model allowing for unWISE incompleteness is …
Figure 11
Figure 11. Figure 11: — Constraints and degeneracies between the derived parameters at 0.55 < z < 0.6. A subscript C denotes the CMASS HOD parameters while a subscript W denotes the unWISE-Blue HOD parameters. The default model is in red, and the model allowing for unWISE incompleteness is…

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