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Photometric Objects Around Cosmic Webs (PAC) Delineated in a Spectroscopic Survey. VIII. Revisiting the Lensing is Low Effect

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Calibrating BOSS galaxies' stellar-to-halo mass relation with PAC clustering measurements yields galaxy-galaxy lensing predictions that agree with HSC, DES, and KiDS, so the 'lensing is low' discrepancy is a modeling artifact, not new…

desk verdict Clustering-calibrated SHAM predicts BOSS GGL without tension, but missing model error bars make the no-tension claim conditional. read the letter →

arxiv 2502.09404 v1 pith:ZT473DDQ submitted 2025-02-13 astro-ph.CO

Xiaolin Luo , Kun Xu , Yipeng Jing , Hongyu Gao , Hekun Li , Donghai Zhao , Jiaxin Han , Chengliang Wei
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Yu Luo
This is my paper · ORCID
classification astro-ph.CO
keywords galaxy-galaxylensingislowgalaxy-haloconnectionsubhaloabundancematchingstellar-to-halomassrelationBOSSgalaxiesS8tensionPACmethod
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 argues that the well-known 'lensing is low' tension, in which observed galaxy-galaxy lensing around BOSS galaxies falls 20-30% below predictions based on Planck cosmology, is largely an artifact of how previous models connected galaxies to dark matter halos. Using PAC measurements, which count photometric galaxies around spectroscopic BOSS galaxies in stellar-mass bins, the authors calibrate a subhalo abundance-matching model with a tightly constrained stellar-to-halo mass relation and stellar mass completeness. Predicted galaxy-galaxy lensing for BOSS CMASS and LOWZ matches measured signals from HSC Y1, DES Y3, and KiDS-1000 down to 0.2 Mpc/h in both WMAP and Planck universes. The best-fit S8 from CMASS lensing is 0.8267 ± 0.0108 combined, leaving Planck and WMAP both viable. The practical upshot is that accurate modeling of the lens population, not baryonic feedback or a lowered S8, removes the small-scale deficit, except for a KiDS small-scale LOWZ offset that the authors flag as needing confirmation.

What carries the argument

The load-bearing object is the PAC-calibrated galaxy-halo connection: the excess surface density n̄2 wp(rp) of photometric galaxies with given stellar masses around BOSS spectroscopic galaxies (42 LOWZ and 33 CMASS measurements), fitted by subhalo abundance matching to a double-power-law stellar-to-halo mass relation M* = 2k / [(Macc/M0)^−α + (Macc/M0)^−β] with log-normal scatter. Combined with the stellar mass completeness of LOWZ and CMASS as a function of redshift (Table D2 of Paper IV), this maps every BOSS galaxy to a central or satellite subhalo in N-body simulations. Predicted lensing is obtained by projecting the galaxy-matter cross-correlation ξgm to get ΔΣ(rp) = Σ(<rp) − Σ(rp), the quantity compared with observed galaxy-galaxy lensing. The SHMR plus completeness, not a tuned HOD, supplies the correct one-halo contribution at rp < 1 Mpc/h, which is the regime where the 'lensing is low' deficit appeared.

What would settle it

A decisive check is to measure BOSS CMASS halo masses independently of the PAC clustering data, for instance by stacking satellite kinematics or using a lensing source catalog with fully independent photometric redshifts, and compare with the PAC stellar-to-halo mass relation; if the independently inferred halo masses are systematically higher at fixed stellar mass, the predicted ΔΣ would be too low and the claimed agreement would be coincidental.

Watch

Extended reading notes

Core claim

The paper's central claim is that the 'lensing is low' discrepancy disappears once the galaxy-halo connection of BOSS galaxies is built from PAC cross-correlation measurements rather than from standard HOD fits. In Paper IV, 42 LOWZ and 33 CMASS excess surface density measurements in stellar-mass bins were modeled by subhalo abundance matching with a double-power-law stellar-to-halo mass relation with scatter, giving percent-level parameter constraints. Here the authors apply that relation plus the stellar mass completeness of the BOSS samples to N-body mock catalogs in CosmicGrowth (WMAP, S8 = 0.785) and Jiutian (Planck 2018, S8 = 0.825), compute the galaxy-galaxy lensing signal ΔΣ(rp) from the galaxy-matter cross-correlation, and compare with measurements from HSC Y1, DES Y3, and KiDS-1000. They find no scale range in which the predicted CMASS signal exceeds the observations, and the LOWZ predictions agree with HSC and DES at rp < 0.6 h−1 Mpc. They conclude that no significant baryon feedback is required to suppress small-scale clustering and that earlier reports of low lensing stem from insufficiently flexible or inaccurate galaxy-halo modeling.

Load-bearing premise

The load-bearing premise is that the stellar-to-halo mass relation, its scatter, the satellite assignment, and the stellar mass completeness derived from the PAC clustering measurements are accurate for BOSS galaxies down to 0.2 Mpc/h; if any of these are wrong, the predicted lensing amplitude and shape shift and the agreement with the observed shear does not actually test the 'lensing is low' claim.

Editorial extensions

If this is right

  • The BOSS CMASS 'lensing is low' deficit disappears at all measured scales down to 0.2 h−1 Mpc once the PAC-calibrated abundance-matching model is used, so the anomaly does not require lowering S8 or adding baryonic suppression.
  • The inferred S8 values from CMASS lensing (0.8294 ± 0.0110 for HSC, 0.8073 ± 0.0372 for DES, 0.8189 ± 0.0440 for KiDS, and 0.8267 ± 0.0108 combined) are consistent with both WMAP and Planck cosmologies at current precision, so these data alone cannot discriminate between the two.
  • Because predicted lensing depends strongly on the redshift-dependent stellar mass completeness, future analyses of samples with rapidly varying completeness, such as CMASS, must model completeness bin by bin rather than for the full redshift range.
  • If the small-scale KiDS-1000 LOWZ measurement is confirmed, it would point to survey-specific systematics or to a genuine baryonic effect at rp < 0.6 h−1 Mpc that the PAC model does not need elsewhere; if not confirmed, the 'lensing is low' problem is fully explained by galaxy-halo modeling.

Reading between the lines

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

  • An implication left implicit is that joint analyses of clustering and lensing that marginalize over standard HOD parameters may systematically underestimate the small-scale one-halo lensing signal; using PAC-style n̄2 wp observables in stellar-mass bins should reduce that bias in future S8 constraints.
  • A natural extension is to apply the same PAC-calibrated abundance matching to the newer DESI lens samples; the paper's logic predicts the 'lensing is low' deficit should also disappear there, which is directly testable with upcoming DESI lensing data.
  • The survey-to-survey spread in fitted S8 suggests that the combined constraint leans heavily on HSC's small error bars; if HSC's shear calibration carries an unknown systematic, the true S8 could be lower and the Planck-versus-WMAP question would remain open even with this model.
  • The present argument does not model baryonic gas explicitly; a hydrodynamical simulation with strong feedback could test whether the small-scale agreement hides a cancellation between baryonic suppression and residual uncertainty in the PAC stellar-to-halo mass relation.
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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

4 major / 5 minor

Summary. This paper revisits the "Lensing is Low" tension by predicting galaxy-galaxy lensing (GGL) signals around BOSS LOWZ and CMASS galaxies using the galaxy-halo connection derived in Paper IV from Photometric objects Around Cosmic webs (PAC) measurements. The authors generate mock catalogs via subhalo abundance matching in two N-body simulations with WMAP (CosmicGrowth) and Planck (Jiutian) cosmologies, then compare the predicted ΔΣ(rp) profiles against HSC Y1, DES Y3, and KiDS-1000 GGL measurements. They report no significant tension between predictions and observations in either cosmology, and they fit S8 = 0.8294 ± 0.0110 (HSC), 0.8073 ± 0.0372 (DES), and 0.8189 ± 0.0440 (KiDS) for CMASS, with a combined value of 0.8267 ± 0.0108. The paper concludes that imprecise galaxy-halo connection modeling in earlier work is the primary cause of the apparent discrepancy, and that strong baryon feedback is not required to match small-scale GGL data.

Significance. If the predicted GGL curves are robust, this result would substantially reframe the "Lensing is Low" discussion by showing that an accurate galaxy-halo connection, constrained without using lensing information, can reproduce the observed amplitudes and scale dependence in both WMAP and Planck cosmologies. The PAC-based SHAM constraints are a genuine independent input, and the comparison to multiple lensing surveys is a strength. The paper also makes a concrete falsifiable prediction: the small-scale GGL signal around BOSS galaxies should follow the presented curves, and future data with smaller errors can discriminate between cosmologies. The claim that baryon feedback is unnecessary is provocative but is only a corollary of the no-tension claim, so its robustness depends on the same error analysis. The work is clearly relevant to the journal's scope in observational cosmology.

major comments (4)
  1. [§4.2, Figures 3–5] The predicted ΔΣ curves are shown as single lines with no uncertainty bands, yet the paper's central conclusion is that "there is no significant tension" between these curves and the observed GGL measurements. The SHMR parameters in Table 1 have MCMC posteriors, and the stellar mass completeness from Table D2 of Paper IV is an inferred quantity, but none of these uncertainties are propagated into the predicted GGL profiles. Without error bands, the statement of no tension is only a visual judgment and cannot be distinguished from the alternative that the model space is flexible enough to accommodate the data. To make the central claim quantitative, the authors should propagate the SHMR posterior and completeness uncertainties into the predicted profiles and report a tension statistic (e.g., chi-square or probability-to-exceed) for each survey and cosmology.
  2. [§4.2, Table 2, Conclusions] The reported S8 values are obtained by fitting the amplitude of the observed GGL signals under the assumption that the predicted amplitude scales as S8^2 at fixed galaxy-halo connection. These constraints are therefore not independent predictions of S8; they are a re-parameterization of the observed GGL amplitude. The abstract and conclusions present these S8 values alongside the "no tension" claim, which risks conflating an a posteriori fit with an a priori prediction. The paper should clearly separate the two statements: the SHMR-derived curves are the independent predictions, while the S8 values are fitted parameters whose only role is to show consistency with the WMAP and Planck cosmologies under the adopted scaling law.
  3. [§4.2, Figure 4] For the LOWZ comparison, the predicted signals are computed for redshift bins 0.2–0.3 and 0.3–0.4, while the observed measurements are for 0.15–0.31 and 0.31–0.43. The text acknowledges this is "an approximation for reference," yet the subsequent sentences state that the predictions "exhibit a higher degree of consistency" and that "no significant tension exists" at large scales for LOWZ. Because the lens sample selection differs between prediction and observation, this comparison cannot support the no-tension claim as stated. The authors should either recompute the predictions for the exact observed redshift bins using the completeness interpolation, or explicitly mark the LOWZ comparison as illustrative and exclude it from the quantitative conclusions.
  4. [§3.1, §4.2, Figure 2] The strong redshift dependence of the predicted GGL signals shown in Figure 2 is driven by the stellar mass completeness, and the CMASS 0.54–0.70 predictions rely on interpolating completeness from Table D2 of Paper IV. The paper does not test the sensitivity of the predicted ΔΣ profiles to plausible variations in this completeness interpolation. Given that a small shift in completeness can change the effective lens redshift distribution and the one-halo term, the authors should include a completeness-variation test (e.g., using the upper and lower edges of the completeness curves or an alternate interpolation scheme) to demonstrate that the no-tension conclusion is robust to this input.
minor comments (5)
  1. [Abstract] The phrase "unless the the GGL observation" contains a duplicated "the"; please correct.
  2. [§5, Figure 5 caption] The word "Compassion" in "Compassion between predicted GGL signals" should be "Comparison".
  3. [§3.1, Eq. (1)] The text defines Macc as "the viral mass of the halo" — "viral" should be "virial".
  4. [§3.2] The text introduces rmax_pi = 50 Mpc/h but the integration variable in Eq. (3) is r_pi; please make the notation consistent and define the line-of-sight integration limits explicitly.
  5. [§4.2] The phrase "we only consider the best-fit value of the SHMR and stellar mass completeness" is important and appears only in the S8 fitting discussion; it should be stated earlier and repeated in the conclusions, since it directly limits the strength of the no-tension claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the GGL predictions are constrained by PAC clustering, a lensing-independent input, and the S8 values are explicitly fits rather than predictions.

full rationale

The derivation chain is not circular. The SHMR and stellar-mass completeness are adopted from Paper IV, where they were fitted to 42/33 PAC nbar2wp(rp) clustering measurements around BOSS galaxies; GGL was not an input to those fits. The mock catalogs therefore yield Delta-Sigma predictions that are externally testable against HSC, DES, and KiDS GGL data. The S8 values quoted in Section 4.2 and Table 2 are explicitly fits to the GGL amplitudes ('we simply assume that the amplitude of these signals at each scale is linearly correlated to S8^2 and fit the value of S8'), not predictions from the model, so presenting them as best-fitting values is accurate. The main caveats—LOWZ redshift bins do not match the observations, and the quoted errors are underestimated because only the best-fit SHMR/completeness and a simple linear model are used—are stated by the authors and concern statistical robustness rather than circular reasoning. Self-citations to Papers I/III/IV supply prior clustering-based inputs that are independent of the lensing data used for comparison, so the central 'no significant tension' claim does not reduce to its own inputs.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities. Its free parameters are the SHMR model parameters fitted to clustering data and the S8 value fitted to lensing data. The main axioms concern the validity of SHAM, the accuracy of stellar mass completeness from prior work, and the fidelity of the simulations used.

free parameters (3)
  • SHMR parameters for CosmicGrowth (WMAP) LOWZ and CMASS: log10 M0, alpha, beta, log10 k, sigma = LOWZ: log10 M0=11.579, alpha=0.429, beta=2.215, log10 k=10.105, sigma=0.201; CMASS: log10 M0=11.624, alpha=0.466…
    These double power law parameters are fitted via MCMC to PAC nbar2 wp measurements and define the mock galaxy populations used to predict GGL.
  • SHMR parameters for Jiutian (Planck) LOWZ and CMASS: log10 M0, alpha, beta, log10 k, sigma = LOWZ: log10 M0=11.641, alpha=0.433, beta=2.119, log10 k=10.121, sigma=0.187; CMASS: log10 M0=11.681, alpha=0.438…
    Re-fitted with the same PAC data in the Jiutian simulation to enable GGL predictions in the Planck cosmology.
  • S8 (combined constraint for CMASS from HSC, DES, KiDS) = 0.8267 +/- 0.0108; separate values: HSC 0.8294 +/- 0.0110, DES 0.8073 +/- 0.0372, KiDS 0.8189 +/- 0.0440
    Fitted to the observed GGL amplitudes by assuming the predicted signal amplitude scales linearly with S8^2. The authors note the errors are underestimated.
assumptions (4)
  • domain assumption Subhalo abundance matching with a double power law SHMR and Gaussian scatter accurately describes the galaxy-halo connection of BOSS galaxies, including on small scales.
    Central modeling assumption of Section 3.1.
  • domain assumption The stellar mass completeness functions from Paper IV (Table D2) are accurate for the BOSS LOWZ and CMASS samples, and interpolation across redshift bins is valid.
    Used in Section 4.2 to generate redshift-dependent mock catalogs.
  • domain assumption The CosmicGrowth and Jiutian N-body simulations, together with HBT+ subhalo finding and the Jiang et al. (2008) orphan treatment, provide converged halo and subhalo statistics.
    Mock catalogs are built from these simulations in Section 3.1.
  • ad hoc to paper The amplitude of the predicted GGL signal at each scale is linearly proportional to S8^2 at fixed galaxy-halo connection.
    Assumed in Section 4.2 for fitting S8.

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Cite this review

Pith. "Pith review of Photometric Objects Around Cosmic Webs (PAC) Delineated in a Spectroscopic Survey. VIII. Revisiting the Lensing is Low Effect." pith.science (2026). https://pith.science/paper/ZT473DDQ

@misc{pith2026250209404,
  author       = {Pith},
  title        = {Pith review of: Photometric Objects Around Cosmic Webs (PAC) Delineated in a Spectroscopic Survey. VIII. Revisiting the Lensing is Low Effect},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZT473DDQ}},
  note         = {Machine review of arXiv:2502.09404}
}
abstract

The issue of over-predicting the galaxy-galaxy lensing (GGL) signal using conventional galaxy-halo connection models has become well-known as the ``Lensing is Low'' problem, which has been extensively investigated using the Baryon Oscillation Spectroscopic Survey (BOSS) galaxy samples. This issue is also tightly related to the so-called $S_8$ tension. By applying our Photometric objects Around Cosmic webs (PAC) method to the BOSS survey and the DESI deep photometric survey, we obtained hundreds of cross-correlation measurements to establish an accurate galaxy-halo connection for BOSS galaxies through the halo abundance matching technique (Paper IV). With this galaxy-halo connection, we show in this work that the predicted GGL signals for BOSS galaxies both in the Planck and WMAP Universes actually agree very well with the GGL measurements. We find the best-fitting value $S_8 = 0.8294 \pm 0.0110$, $0.8073 \pm 0.0372$ and $0.8189 \pm 0.0440$ for the CMASS samples with the source galaxies from HSC, DES and KiDS image surveys, respectively. Our work indicates that accurate modeling of the lens population is so critical to interpret the GGL observation. For the scale of $r_p < 0.6\,h^{-1}\rm{Mpc}$, our GGL prediction for LOWZ samples are also in good agreement with the observations of HSC and DES. However, the GGL observation of KiDS is much lower on the small scale. Our results indicate that no significant baryon feedback is needed to suppress the small scale clustering unless the the GGL observation of KiDS on the small scale will be confirmed.

Figures

Figures reproduced from arXiv: 2502.09404 by the authors.

Figure 1
Figure 1. Stellar mass completeness of the LOWZ (left) and CMASS (right) samples. The data is provided by Table D2 of Paper IV. 10 1 10 0 10 1 rp [Mpc h 1 ] 0 2 4 6 8 10 rp × [1 0 6 M p c 1 ] LOWZ 0.20 - 0.25 0.25 - 0.30 0.30 - 0.35 0.35 - 0.40 0.20 - 0.40 10 1 10 0 10 1 rp [Mpc h 1 ] 0 2 4 6 8 10 rp × [1 0 6 M p c 1 ] CMASS 0.50 - 0.55 0.55 - 0.60 0.60 - 0.65 0.65 - 0.70 0.50 - 0.70 [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. The predicted GGL signals in WMAP cosmology, which yield different completeness across redshift bins. The variation of signals along redshift in CMASS (right panel) is much larger than that in LOWZ (left panel). from the Jiutian simulation exhibit a commensurate in￾crease in amplitude. Since the value of S8 holds signif￾icant sensitivity to the amplitude of GGL signals, we simply assume that the amplitude of these s… view at source ↗
Figure 3
Figure 3. Predicted GGL singals in redshift range 0.54 − 0.70. The predicted signals are derived from Jiutian (cyan solid line) and CosmicGrowth (orange dashed line) simula￾tions with S8 = 0.825 (Planck) and 0.785 (WMAP), respec￾tively. The measurements are presented by Leauthaud et al. (2022) for the CMASS samples with source galaxy from HSC, DES and KiDS surveys in redshift bins 0.54 − 0.70 [PITH_FULL_IMAGE:figures/full_fi… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: GGL measurements for LOWZ galaxies with source galaxy from HSC, DES and KiDS surveys, alongside the predictions of WMAP and Planck cosmology based on the PAC method. 10 0 10 1 rp [Mpc h 1 ] 2 4 6 8 10 12 rp × [M p c 2 ] CMASS 0.54-0.70 Planck Cosmology Amon+23 Planck C…
Figure 5
Figure 5. Figure 5: Compassion between predicted GGL signals and measured signals using source galaxies from HSC Y1 and DES Y3 + KiDS-1000 for the results of CMASS samples in Amon et al. (2023). It is evident from the analysis that the HODs de￾rived from the CosmicGrowth and Jiutian simul…
Figure 6
Figure 6. Figure 6: HODs for CMASS samples derived from our SHMR after taking the stellar mass completeness into account. The HODs presented by Amon et al. (2023) in Lensing cosmology are compared with our results in WMAP (left panel) and Planck (right panel) cosmology. connection model b…

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