{"id":"75b083ba-7f63-447c-8728-9901693c0efd","arxiv_id":"2502.02744","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":11,"one_line_summary":"Cross-correlating unWISE-Blue with BOSS CMASS in narrow redshift bins yields an evolving halo occupation distribution, with unWISE-Blue mean halo mass and satellite fraction declining toward higher redshift.","lead":"The paper uses cross-correlations between the unWISE-Blue infrared galaxy sample and BOSS CMASS galaxies with measured distances to measure how unWISE-Blue galaxies populate dark matter halos at different redshifts. It is useful because it gives the first redshift-resolved halo occupation measurement of this full-sky sample, which is used in many cosmological cross-correlation studies.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The fixed-zero occupation correlation coefficients Rcs/Rss/Rsc in §4.2 are an untested assumption that directly enters the 1-halo cross-correlation; if unWISE-Blue and CMASS halos are correlated, the inferred unWISE-Blue bias, halo mass, and satellite fraction could shift by more than the quoted…","rationale":"The reader's weakest_assumption is the same as the most load-bearing concern I find. The cross-correlation 1-halo term is the only place where the HODs of the two populations are coupled, and the mixed occupation moments are exactly where Rcs/Rss/Rsc enter. The paper acknowledges the simplification but does not bound its effect. The lack of an unWISE auto-correlation measurement makes the degeneracy irreducible: the cross-correlation amplitude on small scales is compatible with a range of (unWISE satellite occupation, occupation correlation) pairs. Because the overlap between CMASS and unWISE halo populations evolves with redshift, the bias could masquerade as the reported HOD evolution. I agree with the reader's conditional verdict; the concern does not change the verdict, but the paper should add a robustness test or at least an explicit caveat quantifying possible shifts.","tokens_in":26730,"tokens_out":9747,"duration_ms":100402,"concrete_test":"Re-run the six redshift-bin fits with Rcs, Rss, Rsc sampled over [-1, 1] (or at least fixed to +1 and -1) alongside the ten HOD parameters, then compare the marginalized unWISE-Blue bias, mean halo mass, and satellite fraction to Tables 3 and 5. If any derived parameter shifts by more than its quoted 1σ in two or more bins, the independent-occupation assumption is load-bearing and must be quoted as a systematic. A complementary check is to fit the same model to mock catalogs built with known correlated occupations and verify recovery.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Eq. 26, the 1-halo cross-power is P12^1h(k) = ∫ n(M) u(k|M) [Ns,1 Ns,2 u(k|M) + <Nc,1 Ns,2> + <Nc,2 Ns,1>] dM. Setting Rcs = Rss = Rsc = 0 factorizes these mixed occupation moments. Both samples occupy similar-mass halos (CMASS mean halo mass ~13.55, unWISE-Blue ~13.3 in Tables 2 and 3), so correlated occupation is physically plausible. The paper explicitly leaves this to future work, but no unWISE autocorrelation is included, so the cross-correlation alone cannot fully separate unWISE satellite occupation from the correlation coefficients; the unWISE HOD is not uniquely determined without this assumption. The effect can be redshift-dependent because the mass overlap between CMASS and unWISE host halos changes across 0.45 < z < 0.75, which would directly contaminate the claimed HOD evolution. The COSMOS n(z) systematics are secondary; the fixed-zero occupation assumption is the first untested approximation that would change the central science result.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":27120,"tokens_out":4477,"duration_ms":42220,"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":[{"comment":"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.","section":"Section 4.2, Eq. (26)"},{"comment":"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.","section":"Section 2.1, Eq. (38)"},{"comment":"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.","section":"Section 5.2.1, Table 3"}],"minor_comments":[{"comment":"Typo: 'magnificantion' should be 'magnification' in the sentence introducing the binned model.","section":"Section 4.3.5"},{"comment":"Typo: 'occurr' should be 'occur' in the caption.","section":"Fig. 9 caption"},{"comment":"Typo: 'background' is misspelled as 'backgpround' in the sentence about the cosmic infrared background.","section":"Section 1"},{"comment":"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.","section":"Section 3"},{"comment":"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.","section":"Section 4.3.4"}],"recommendation":"major_revision","confidential_remarks":"The paper is a competent and useful methodological contribution, and the data treatment is thorough. The main risk to the central claim is the untested assumption of uncorrelated occupations (Rcs=Rss=Rsc=0). This is a standard limitation in cross-correlation HOD analyses, but because the paper's headline result is the redshift evolution of the unWISE-Blue HOD, the authors should be required to demonstrate that their conclusion is robust to relaxing this assumption or at least quantify the resulting systematic uncertainty. The non-monotonicity of the derived parameters in Table 3 also warrants a more careful significance assessment before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is the first redshift-resolved HOD fit for unWISE-Blue, and the machinery (post-Limber, RSD, halo exclusion applied to a photometric-spectroscopic cross-correlation) is genuinely new and mostly well executed. The paper is worth taking seriously. The headline result – mild evolution in unWISE-Blue bias and halo mass – is plausible but sits on an assumption the authors themselves flag: Rcs = Rss = Rsc = 0 in Eq. 26. Since CMASS and unWISE-Blue live in similar-mass halos, correlated occupation is physically reasonable, and the cross-correlation alone cannot separate unWISE satellite occupation from these correlation coefficients. The authors leave this to future work; the consequence is that the claimed redshift evolution, especially the satellite fraction drop, is not yet uniquely determined. I don't think this is fatal – it's a clearly stated limitation, and the rest of the model is careful – but it is load-bearing for the central science claim.\n\nWhat's good: the treatment of systematics is thorough. Fiber collisions, imaging systematics, magnification (with the aperture correction), integral constraint, jackknife covariance with the Percival et al. Gaussian correction – all handled explicitly. The CMASS HOD matches White et al., Reid et al., Saito et al., etc., which validates the machinery. The code is public. The comparison with Kusiak et al. is fair. The paper is clear about what is new and what builds on previous work.\n\nSoft spots beyond the occupation correlation: the unWISE n(z) is from a 2 deg^2 COSMOS field and its uncertainty is not propagated into the HOD posteriors. That's a real but secondary issue. Also the abstract summarizes the bias evolution as a monotonic drop from b=1.6 to b=1.4, while Table 3 shows b=1.63 at 0.50<z<0.55 and b=1.64 at 0.70<z<0.75 – the trend is not strictly monotonic. That's a minor over-simplification, not a flaw. The incompleteness test (finc marginalization) is a good robustness check and shows the derived parameters are stable.\n\nWho this is for: anyone building mocks for unWISE-Blue, or working on clustering redshifts or photometric-spectroscopic cross-correlations. The method section is transferable.\n\nRecommendation: send to peer review. The Rcs/Rss/Rsc assumption should be pushed on in the report – a sensitivity test, or at least an explicit statement of how the HOD parameters shift if the coefficients are allowed to vary with a simple model. But this is a legitimate, well-documented measurement that deserves referee time.","headline":"Solid tomographic HOD work whose central unWISE-Blue evolution result is conditional on an untested occupation-correlation assumption; worth refereeing, not desk-rejecting.","tokens_in":27634,"tokens_out":2062,"would_cite":true,"duration_ms":19151,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["halo occupation distribution","galaxy clustering","cross-correlation","photometric redshifts","unWISE","BOSS CMASS","tomographic analysis","halo model"],"falsifier":"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.","tokens_in":26531,"feed_emoji":"🔭","tokens_out":10009,"duration_ms":82465,"temperature":0.7,"pith_summary":"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.","feed_headline":"Cross-correlations reveal lighter halos for unWISE-Blue at high redshift","feed_subtitle":"A photometric-spectroscopic halo model finds bias falling from 1.6 to 1.4 and satellite fractions halving between z=0.45 and 0.75.","key_machinery":"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 $10\\,h^{-1}\\,\\mathrm{Mpc}$.","core_discovery":"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 $10\\,h^{-1}\\,\\mathrm{Mpc}$.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the five-parameter HOD parametrization that the paper uses to describe the number of central and satellite galaxies as a function of halo mass.","marker":"Zheng et al. 2007"},{"why":"Provides the HALOMOD halo-model code and base formulas for the one-halo and two-halo power spectra that the paper modifies for cross-correlations.","marker":"Murray et al. 2021"},{"why":"Provides the post-Limber integral used in place of the Limber approximation, which is inadequate for narrow spectroscopic redshift bins.","marker":"Simon 2007"},{"why":"Supplies the Ng-Matched halo exclusion scheme and scale-dependent bias used in the two-halo term.","marker":"Tinker et al. 2005"},{"why":"Provides the linear redshift-space distortion model applied to the angular correlation function.","marker":"Kaiser 1987"},{"why":"Defines the unWISE-Blue sample, its color cuts, redshift distribution, number-count slope, and previous bias constraints.","marker":"Krolewski et al. 2020"},{"why":"Provides the previous redshift-independent unWISE-Blue HOD measurement from the angular autocorrelation and CMB lensing cross-correlation, which this paper extends by adding tomographic redshift information.","marker":"Kusiak et al. 2022"},{"why":"Quantifies CMASS high-mass incompleteness, which the paper uses to model the CMASS HOD through the $f_{\\mathrm{inc}}$ correction.","marker":"Leauthaud et al. 2016"}],"fun_headline_variants":["unWISE-Blue halo masses drop, satellites halve at high z","Bias falls 1.6 to 1.4 for unWISE-Blue from z=0.5 to 0.7","Photometric-spectroscopic halo model shows unWISE-Blue HOD evolves","New cross-correlation method probes unWISE-Blue halo evolution","Satellite fraction in unWISE-Blue halves from 20% to 10% by z=0.7"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["unWISE-Blue halo masses drop, satellites halve at high z","Bias falls 1.6 to 1.4 for unWISE-Blue from z=0.5 to 0.7","Photometric-spectroscopic halo model shows unWISE-Blue HOD evolves","New cross-correlation method probes unWISE-Blue halo evolution","Satellite fraction in unWISE-Blue halves from 20% to 10% by z=0.7"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000881,"raw_usage":{"total_tokens":3963,"prompt_tokens":1259,"completion_tokens":2704,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":875,"completion_tokens_details":{"reasoning_tokens":2582}},"tokens_in":875,"tokens_out":2704,"duration_ms":20018,"temperature":1.0,"reasoning_tokens":2582,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T11:16:32.662632+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"L., & Zehavi, I","cited_arxiv_id":null,"evidence_quote":"Supplies the five-parameter HOD parametrization that the paper uses to describe the number of central and satellite galaxies as a function of halo mass."},{"cited_title":"2021, Astronomy and Computing, 36, 100487","cited_arxiv_id":null,"evidence_quote":"Provides the HALOMOD halo-model code and base formulas for the one-halo and two-halo power spectra that the paper modifies for cross-correlations."},{"cited_title":"L., Weinberg, D","cited_arxiv_id":null,"evidence_quote":"Supplies the Ng-Matched halo exclusion scheme and scale-dependent bias used in the two-halo term."},{"cited_title":"F., & White, M","cited_arxiv_id":null,"evidence_quote":"Defines the unWISE-Blue sample, its color cuts, redshift distribution, number-count slope, and previous bias constraints."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the previous redshift-independent unWISE-Blue HOD measurement from the angular autocorrelation and CMB lensing cross-correlation, which this paper extends by adding tomographic redshift information."},{"cited_title":"2016, MNRAS, 457, 4021","cited_arxiv_id":null,"evidence_quote":"Quantifies CMASS high-mass incompleteness, which the paper uses to model the CMASS HOD through the $f_{\\mathrm{inc}}$ correction."}],"review_version":1}