The Hydrostatic Mass Bias and the $\sigma_8$ Tension: A Multi-Probe Forecast for Stage-IV/V Surveys

Ayodeji Ibitoye; Prabhakar Tiwari; Qi Xiong; Yan Gong

REVIEW

The Hydrostatic Mass Bias and the $\sigma_8$ Tension: A Multi-Probe Forecast for Stage-IV/V Surveys

Ayodeji Ibitoye, Prabhakar Tiwari, Qi Xiong, Yan Gong

Cosmology and Nongalactic Astrophysics · Submitted 23 Feb 2026 · 2 references

Pith's verdict: The paper's main result—SO+LSST reaching 0.98% on bHSE—rests on an SO noise level (1.2 µK-arcmin) that contradicts the paper's own quoted SO spec (8–10 µK-arcmin), so the headline precision is not credible as written.

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arXiv ID2602.19478 (version 2)

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CitationAyodeji Ibitoye, Prabhakar Tiwari, Qi Xiong, Yan Gong. "The Hydrostatic Mass Bias and the $\sigma_8$ Tension: A Multi-Probe Forecast for Stage-IV/V Surveys." arXiv:2602.19478 (2026). https://pith.science/paper/ETUO4BGU

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Editor's note

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Short version: this is a well-structured Fisher forecast for an important question—whether tomographic tSZ–galaxy–shear cross-correlations can calibrate the hydrostatic mass bias in Stage-IV surveys. The modeling is standard but careful, with realistic foregrounds, baryonic feedback, per-bin nuisance parameters, and a useful probe decomposition. The specific combination (tomographic 6x2pt with tSZ) appears genuinely new relative to the cited forecasts, and the paper makes a commendable effort with robustness tests.

The problem is the headline number. The paper claims SO+LSST gives σ(bHSE)=0.00195 (0.98%), but that forecast is generated with an SO LAT white-noise level of 1.2 µK-arcmin at 145 GHz (Table 1, Eq. 11, §4.4, §5.1). The same paper says in §3.2.1 that SO has 8.0/10.0 µK-arcmin for the LAT, matching the published Simons Observatory baseline. Using 1.2 instead of ~10 reduces the noise power by a factor of ~70 in the tSZ channel, and since bHSE information is carried mainly by the tSZ amplitude, the precision is inflated by roughly the same factor in S/N. This is not a minor typo: it makes the difference between a sub-percent headline and a more plausible few-percent constraint. The CMB-S4 numbers, which use 1.0 µK-arcmin (close to the Science Book spec), are less affected.

There are other soft spots. The GNFW pressure normalization (P0, c500) is fixed to Arnaud et al. (2010), so the 0.98% constraint is really on bHSE times the pressure amplitude; if P0 is uncertain at the few-percent level—typical for ICM modeling—the claimed 'pure' bHSE calibration is overstated. The paper also models bHSE as constant, then in §5.3 explains tomography's power by saying bHSE varies with mass/redshift; that's an internal contradiction, even if tomography would help under the constant model for other reasons. The 'factor of three' tomography improvement in the abstract is not consistent with Table 1, which shows 1.4× to 5× depending on the combination.

The paper deserves a serious referee—the framework is reusable and the question is timely—but it needs major revision. The referee should ask for the SO noise to be corrected and the forecast re-run, and for the GNFW normalization to be varied or the interpretation toned down.

Referee report

Significance

If the forecast is correct, it would establish that Stage-IV surveys can calibrate b_HSE to sub-percent precision, turning a leading cluster-cosmology systematic into a well-measured parameter. The paper uses a standard Fisher formalism, includes a realistic set of systematics, and provides useful quantitative comparisons of survey combinations. However, the headline numerical claim is load-bearing and currently rests on an internally inconsistent SO noise specification and on fixing the GNFW pressure-profile normalization at its fiducial value. Both issues directly affect what the 0.98% number represents, so the significance of the result as stated is not yet established. The paper's strengths are its comprehensiveness and the transparent presentation of the pipeline; its main weakness is that the central forecast has not been tested against the paper's own stated survey parameters.

Major objections (3)

[§3.2.1 vs. Table 1 / Eq. (11)] The SO+LSST headline constraint uses an SO LAT white-noise level of 1.2 µK-arcmin at 145 GHz (Table 1; Eq. 11; quoted again in §4.4 and §5.1). This contradicts §3.2.1, which states that SO delivers 'higher noise (8.0/10.0 µK-arcmin, respectively)' and cites the SO baseline (Ade et al. 2019). The factor (10/1.2)^2≈69 in noise power enters Γ_ℓ in Eq. (14), and b_HSE information is carried predominantly by the tSZ amplitude in C_yy, C_yg, and C_yγ. Using 1.2 instead of ~10 µK-arcmin therefore substantially inflates the claimed signal-to-noise on b_HSE. Please rerun the forecast with the SO LAT noise level stated in §3.2.1 and report whether the sub-percent result survives.
[§4.5 / Eq. (23)] The GNFW pressure-profile parameters P0 and c500 are fixed to the X-ray-calibrated values of Arnaud et al. (2010). In the model, b_HSE enters the tSZ spectra only through the factors (1−b_HSE)^{10/3} and (1−b_HSE)^{5/3} (Eq. 23). An unknown overall pressure normalization P0 is therefore nearly perfectly degenerate with b_HSE in the tSZ amplitude. The claimed σ(b_HSE)=0.00195 is thus a conditional forecast for b_HSE given a perfectly known pressure profile, not a forecast for b_HSE alone. The text in §4.5 says 'uncertainty is absorbed by b_HSE and GNFW parameters', but those parameters are not varied in the Fisher matrix. The forecast should either marginalize over P0 (and ideally c500) with a realistic prior, or explicitly identify the result as a joint b_HSE×P0 constraint. The robustness tests in §4.6 do not address this.
[§5.3 vs. §2.2.1] The paper motivates tomography by arguing that 'hydrostatic mass bias varies with cluster mass (and thus redshift)' and that this redshift dependence is what separates b_HSE from σ8. However, §2.2.1 models b_HSE as a single, redshift- and mass-independent parameter. If b_HSE is constant, there is no redshift-varying b_HSE signal to distinguish from σ8, so the stated physical mechanism for the tomographic gain is internally inconsistent. The numerical improvement from tomography may come from other redshift-dependent degeneracies, but the explanation in §5.3 needs to be corrected or the model must be generalized to a redshift/mass-dependent b_HSE.

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The paper

The paper claims

Tomographic cross-correlations of the tSZ effect, galaxy clustering, and weak lensing can constrain the hydrostatic mass bias to 0.98% precision, according to Fisher forecasts for Stage-IV surveys.

The reading

The paper argues that the hydrostatic mass bias — the systematic offset between true cluster masses and masses inferred assuming hydrostatic equilibrium — can be measured to sub-percent precision by combining next-generation CMB and optical surveys through tomographic cross-correlations. Its Fisher forecasts, which marginalize over cosmological parameters, galaxy bias, photometric redshift shifts, intrinsic alignments, and baryonic feedback, predict a 0.98% constraint for Simons Observatory plus LSST, with 1.60% for CMB-S4 plus LSST and 2.40% for CMB-S4 plus CSST. Redshift tomography is the key: it improves precision by factors of roughly 2.5–3 over single-bin analyses by breaking the degeneracy between bHSE and σ8. A precise bHSE would remove a leading systematic from cluster cosmology and help decide whether the σ8 tension reflects new physics or an astrophysical miscalibration.

What carries the argument

The machinery is a halo-model pipeline that computes all six auto- and cross-power spectra of the tSZ field (y), galaxy density (g), and weak lensing shear (γ), projected with the Limber approximation and combined in a Fisher matrix with realistic noise and foreground models. The load-bearing element is the differential bHSE scaling between tSZ-containing spectra and optical auto-spectra, together with tomographic binning (5 source bins, 6–10 lens bins) that exploits the redshift-dependent apparent amplitude of the tSZ signal to break the bHSE–σ8 degeneracy.

Extended reading notes

Core claim

The central claim is that the tSZ–galaxy–shear combination, treated tomographically, can turn the hydrostatic mass bias from a nuisance parameter into a precision measurement. Because the tSZ auto-spectrum scales as (1−bHSE)^10/3 and the tSZ–optical cross-spectra as (1−bHSE)^5/3, while galaxy clustering and shear spectra are unaffected, the amplitude of bHSE leaves a distinctive trace that can be separated from σ8 using redshift-dependent information. The authors forecast that SO+LSST tomography reaches σ(bHSE)=0.00195 (0.98%) after full marginalization, and that removing external CMB priors degrades this only to 1.00%, indicating the cross-correlations themselves carry the calibration.

Load-bearing premise

The gas-pressure profile of clusters is held fixed to X-ray-calibrated universal values, so the forecast percent-level constraint is really a joint constraint on bHSE and the unknown overall pressure amplitude; if that amplitude shifts by a few percent, the sub-percent precision on bHSE alone does not follow.

Editorial extensions

If this is right

The hydrostatic mass bias would cease to be a limiting systematic in cluster cosmology; the paper projects it could be measured to 0.98% precision rather than the current ~4–10%.
The bHSE–σ8 degeneracy is broken, so cluster-based measurements of σ8 after marginalizing over bHSE reach ~0.1% precision, tightening tests of the σ8 tension.
Tomographic binning is essential: non-tomographic analyses degrade bHSE constraints by factors of 2.5–3, so future analyses should adopt fine redshift binning.
Optical-only probes (galaxy clustering plus cosmic shear, 3×2pt) do not constrain bHSE at all; including tSZ-containing spectra is necessary, and tSZ–galaxy cross-correlations carry the majority of the information.

Reading between the lines

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

The paper leaves implicit that the 0.98% number measures bHSE only if the gas pressure profile is exactly known; treating P0 and c500 as free parameters would likely inflate the uncertainty, so the sub-percent claim is best read as a joint calibration of mass bias and pressure amplitude.
The differential scaling argument could be pushed further to constrain redshift- or mass-dependent bHSE—the tomographic bins already separate the redshift-varying apparent amplitude from the redshift-constant σ8.
If realized, this self-calibration would let cluster abundance analyses drop their dependence on external X-ray/SZ scaling relations, sharpening σ8 measurements from clusters independent of the tension's resolution.

Original abstract

The hydrostatic mass bias ($b_{\mathrm{HSE}}$) is a leading systematic uncertainty in cluster cosmology and a principal source of degeneracy with $\sigma_8$ and $\Omega_m$. We investigate the capability of Stage-IV CMB and optical surveys to calibrate $b_{\mathrm{HSE}}$ using tomographic cross-correlations between the thermal Sunyaev--Zel'dovich (tSZ) effect, galaxy clustering, and weak lensing. We perform a Fisher forecast incorporating realistic survey noise, foreground modeling for clustered CIB and radio sources, and full marginalization over cosmological and astrophysical nuisance parameters, including per-bin galaxy bias perturbations, photometric redshift shifts, intrinsic alignments, and baryonic feedback modeled with HMCode2020. With optimized tomographic binning (10 lens and 5 source bins for LSST; 6 lens and 5 source bins for CSST), we forecast marginalized constraints of $0.98\%$ for SO+LSST, $1.60\%$ for CMB-S4+LSST, and $2.40\%$ for CMB-S4+CSST. Tomography improves $b_{\mathrm{HSE}}$ precision by factors of approximately three relative to non-tomographic analyses, reflecting the role of redshift information in breaking the $b_{\mathrm{HSE}}$--$\sigma_8$ degeneracy. Optical-only probes provide no direct constraint on $b_{\mathrm{HSE}}$, whereas inclusion of tSZ-containing spectra enables percent-level calibration under realistic systematic assumptions. The results demonstrate that multi-probe tomographic analyses with Stage-IV surveys can achieve robust control of hydrostatic mass bias, strengthening cluster-based constraints on structure growth.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,113 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.52 · human participants 0.01 · controlled comparison 0.53 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.86 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

The hydrostatic mass bias ($b_{\mathrm{HSE}}$) is a leading systematic uncertainty in cluster cosmology and a principal source of degeneracy with $\sigma_8$ and $\Omega_m$. We investigate the capability of Stage-IV CMB and optical surveys to calibrate $b_{\mathrm{HSE}}$ using tomographic cross-correlations between the thermal Sunyaev--Zel'dovich (tSZ) effect, galaxy clustering, and weak lensing. We perform a Fisher forecast incorporating realistic survey noise, foreground modeling for clustered CIB and radio sources, and full marginalization over cosmological and astrophysical nuisance parameters, including per-bin galaxy bias perturbations, photometric redshift shifts, intrinsic alignments, and baryonic feedback modeled with HMCode2020. With optimized tomographic binning (10 lens and 5 source bins for LSST; 6 lens and 5 source bins for CSST), we forecast marginalized constraints of $0.98\%$ for SO+LSST, $1.60\%$ for CMB-S4+LSST, and $2.40\%$ for CMB-S4+CSST. Tomography improves $b_{\mathrm{HSE}}$ precision by factors of approximately three relative to non-tomographic analyses, reflecting the role of redshift information in breaking the $b_{\mathrm{HSE}}$--$\sigma_8$ degeneracy. Optical-only probes provide no direct constraint on $b_{\mathrm{HSE}}$, whereas inclusion of tSZ-containing spectra enables percent-level calibration under realistic systematic assumptions. The results demonstrate that multi-probe tomographic analyses with Stage-IV surveys can achieve robust control of hydrostatic mass bias, strengthening cluster-based constraints on structure growth.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The hydrostatic mass bias ($b_{\mathrm{HSE}}$) is a leading systematic uncertainty in cluster cosmology and a principal source of degeneracy with $\sigma_8$ and $\Omega_m$.	background 1.00	0.05	0.03	asserted 1.00
s1	We investigate the capability of Stage-IV CMB and optical surveys to calibrate $b_{\mathrm{HSE}}$ using tomographic cross-correlations between the thermal Sunyaev--Zel'dovich (tSZ) effect, galaxy clustering, and weak lensing.	contribution 0.94	0.68	0.04	asserted 0.67
s2	We perform a Fisher forecast incorporating realistic survey noise, foreground modeling for clustered CIB and radio sources, and full marginalization over cosmological and astrophysical nuisance parameters, including per-bin galaxy bias perturbations, photometric redshift shifts, intrinsic alignments, and baryonic feedback modeled with HMCode2020.	method 0.99	0.94	0.04	asserted 0.98
s3	With optimized tomographic binning (10 lens and 5 source bins for LSST; 6 lens and 5 source bins for CSST), we forecast marginalized constraints of $0.98\%$ for SO+LSST, $1.60\%$ for CMB-S4+LSST, and $2.40\%$ for CMB-S4+CSST.	result 1.00	0.92	0.19	asserted 0.93
s4	Tomography improves $b_{\mathrm{HSE}}$ precision by factors of approximately three relative to non-tomographic analyses, reflecting the role of redshift information in breaking the $b_{\mathrm{HSE}}$--$\sigma_8$ degeneracy.	interpretation 0.57	0.88	0.18	asserted 0.98
s5	Optical-only probes provide no direct constraint on $b_{\mathrm{HSE}}$, whereas inclusion of tSZ-containing spectra enables percent-level calibration under realistic systematic assumptions.	result 0.91	0.80	0.16	asserted 1.00
s6	The results demonstrate that multi-probe tomographic analyses with Stage-IV surveys can achieve robust control of hydrostatic mass bias, strengthening cluster-based constraints on structure growth.	interpretation 0.99	0.86	0.89	asserted 1.00

What kind of paper the classifier reports this is: simulation study 0.79 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

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S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Stacked panels showing the sensitivity of each probe and cross-probe combination of the angular power spectra (Dℓ = ℓ(ℓ + 1)Cℓ/(2π)) for auto- and crosscorrelations of the thermal Sunyaev-Zel’dovich (tSZ, y), galaxy clustering (g), and cosmic shear (γ) to the amplitude of matter density fluctuations (σ8), with all other cosmological parameters (e.g., Ωm, h, ns) held fixed. APS and CPS represents angular power spectrum and cross-power spectrum, respectively

**Figure 2.** Normalized redshift distributions for LSST Year 10 and CSST. All distributions satisfy ∫ n(z) dz = 1, where n(z) denotes the normalized redshift distribution (total: n(z), tomographic bins: n(z|bin)). Distributions include photometric redshift uncertainties convolved via the error-function formalism of Ma et al. (2006): σz = 0.05(1+z) (LSST sources), σz = 0.03(1+z) (LSST lenses), and CSST values from mission forecasts (σz = 0.05(1+z) sources, σz = 0.03(1+z) lenses; Gong et al. 2019). Top row (Overplotted Totals): Direct comparison of total distributions. Left: CSST sources extend to…

**Figure 3.** Analysis pipeline for forecasting hydrostatic mass bias (bHSE) constraints. The workflow progresses from survey specification through tomographic/non-tomographic analysis of multi-probe power spectra to final marginalized cosmological constraints. Tomographic analyses achieve high-precision bHSE constraints for SO+LSST (0.98% precision), with competitive results for CMB-S4+LSST (1.60%) and CMB-S4+CSST (2.40%). and non-linear regimes while limiting sensitivity to the most foreground-dominated angular scales. 3.2. Survey Specifications 3.2.1. CMB Experiments CMB-S4 is a next-generation

**Figure 4.** Constraints on hydrostatic mass bias (bHSE) from Fisher matrix forecasts of CMB-optical cross-correlations, comparing CMB-S4 + CSST, CMB-S4 + LSST, and SO + LSST. Main panel: 68% and 95% confidence contours in the σ8–bHSE plane. Solid/dashed curves denote tomography (CSST: 6+5 bins, LSST: 10+5 bins)/no-tomography configurations. Color coding: CMB-S4 + CSST (blue), CMB-S4 + LSST (orange), SO + LSST (purple). The black star marks the fiducial cosmology (σ8 = 0.811, bHSE = 0.2), consistent with the CMB-S4 Science Bookffs adopted cluster mass model. Inset: Relative bHSE precision (1σ…

**Figure 5.** Multi-parameter constraints from cross-correlation analyses combining CMB and optical surveys. The corner plot shows 1σ and 2σ confidence contours for five selected cosmological and astrophysical parameters: the matter fluctuation amplitude σ8, hydrostatic mass bias bHSE, matter density Ωm, Hubble constant h, and intrinsic alignment amplitude AIA. Four survey configurations are compared: CMB-S4 + CSST without tomography (blue dashed), CMB-S4 + CSST with tomography (blue solid), CMB-S4 + LSST with tomography (orange solid), and SO + LSST with tomography (purple solid). The…

**Figure 6.** Constraints on galaxy bias perturbation nuisance parameters δb(i) g for tomographic survey combinations: SO+LSST (purple), CMB-S4+LSST (orange), and CMB-S4+CSST (blue). Results are shown for 10 lens redshift bins, with violin plots representing 1σ uncertainty distributions. Annotations in the top-left report the average uncertainty ⟨σ(δbg)⟩ for each survey and its percentage change relative to the SO+LSST baseline (purple). The horizontal gray dashed line marks the fiducial zero value for all bias perturbations

**Figure 7.** Constraints on photometric redshift shift nuisance parameters for tomographic survey combinations: SO+LSST (purple), CMB-S4+LSST (orange), and CMB-S4+CSST (blue). Violin plots show 1σ uncertainty distributions for each redshift bin. Left: Lens photo-z shifts ∆z (i) lens across 10 lens redshift bins. Right: Source photo-z shifts ∆z (i) source across 5 source redshift bins. Annotations in the top-left of each panel report the average uncertainty ⟨σ(∆z)⟩ and percentage changes relative to the SO+LSST baseline. The horizontal gray dashed lines mark the fiducial zero shift value

Figures reproduced from arXiv:2602.19478 by the authors.

References

Works cited (2)

[1]

Abazajian, K., Addison, G., Adshead, P., et al. 2019, arXiv e-prints, arXiv:1907.04473, doi: 10.48550/arXiv.1907.04473 Abazajian, K., Abdulghafour, A., Addison, G. E., et al. 2022a, arXiv e-prints, arXiv:2203.08024, doi: 10.48550/arXiv.2203.08024 Abazajian, K., Addison, G. E., Adshead, P., et al. 2022b, ApJ, 926, 54, doi: 10.3847/1538-4357/ac1596 Abbott, ...

View on Pith Pith review arXiv doi:10.48550/arxiv.1907.04473 2019
[7]

Constraints on photometric redshift shift nuisance parameters for tomographic survey combinations: SO+LSST (purple), CMB-S4+LSST (orange), and CMB-S4+CSST (blue). Violin plots show 1 σ uncertainty distributions for each redshift bin. Left: Lens photo-z shifts ∆z(i) lens across 10 lens redshift bins. Right: Source photo-z shifts ∆z(i) source across 5 sourc...

View on Pith doi:10.48550/arxiv.2509.08673 2011

How the literature uses it

What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 12 sentences without a confident label

Uses the method or tool of 5 papers

The 1-halo and 2-halo terms are computed using the halo model framework implemented in the Core Cosmology Library (CCL; [ref] ), which follows the standard formalism of [ref] .

Halo Models of Large Scale Structure · 1-Halo and 2-Halo Contributions · 1.00
For the tSZ effect, the intracluster medium pressure follows a Generalized NFW (GNFW) profile [ref] , the frequency dependence of the tSZ signal is accounted for in the map and noise modeling.

Testing X-ray Measurements of Galaxy Clusters with Cosmological Simulations · 1-Halo and 2-Halo Contributions · 0.96
Baryonic feedback is modeled via HMCode2020 [ref] , parameterized by $log_10(T_AGN/K)$ (fiducial = 7.8, Gaussian prior $σ=0.3$ from BAHAMAS simulations).

HMcode-2020: Improved modelling of non-linear cosmological power spectra with baryonic feedback · Systematics and Prior Choices · 0.99

Uses data or values from 2 papers

Fiducial values (e.g., $b_HSE=0.2$, $σ_8=0.811$) follow Planck 2018 $Λ$CDM [ref] cluster mass calibration studies.

Planck 2018 results. VI. Cosmological parameters · Systematics and Prior Choices · 0.99
Recent cosmological hydrodynamical simulations, such as FLAMINGO and The Three Hundred Project, have quantified $b_HSE$ and its scatter finding a typical value of $1 - b_HSE ∼0.7$–$0.8$ and a complex dependence on cluster dynamical state [ref] .

Hydrostatic mass bias for galaxy groups and clusters in the FLAMINGO simulations · Introduction · 0.81

Cites as support 1 paper

As demonstrated by [ref] and others [ref] , even this evolving tension can be reconciled within $Λ$CDM if the $b_HSE$ mass bias is significantly higher than canonical simulation calibrations, highlighting a profound degeneracy between $b_HSE$ and $σ_8$.

2509.08673 · Introduction · 0.98

Cites as background 1 paper

Their abundance as a function of mass and redshift is exquisitely sensitive to the parameters governing the background cosmology and the growth of structure, most notably the total matter density $Ω_m$ and the amplitude of matter fluctuations, $σ_8$ [ref] .

Cosmological Parameters from Observations of Galaxy Clusters · Introduction · 0.91

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

Abazajian, K., Addison, G., Adshead, P., et al. 2019, arXiv e-prints, arXiv:1907.04473, doi: 10.48550/arXiv.1907.04473 Abazajian, K., Abdulghafour, A., Addison, G. E., et al. 2022a, arXiv e-prints, arXiv:2203.08024, doi: 10.48550/arXiv.2203.08024 Abazajian, K., Addison, G. E., Adshead, P., et al. 2022b, ApJ, 926, 54, doi: 10.3847/1538-4357/ac1596 Abbott, ...

View on Pith Pith review arXiv doi:10.48550/arxiv.1907.04473 2019

[2] [7]

Constraints on photometric redshift shift nuisance parameters for tomographic survey combinations: SO+LSST (purple), CMB-S4+LSST (orange), and CMB-S4+CSST (blue). Violin plots show 1 σ uncertainty distributions for each redshift bin. Left: Lens photo-z shifts ∆z(i) lens across 10 lens redshift bins. Right: Source photo-z shifts ∆z(i) source across 5 sourc...

View on Pith doi:10.48550/arxiv.2509.08673 2011