Constraining the properties of gaseous halos via cross-correlations of upcoming galaxy surveys and thermal Sunyaev-Zel'dovich maps

E.J. Baxter; J.C. Hill; S. Pandey

REVIEW 3 major objections 4 minor 85 references

Constraining the properties of gaseous halos via cross-correlations of upcoming galaxy surveys and thermal Sunyaev-Zel'dovich maps

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Cross-correlating galaxies with CMB maps can rule out feedback models.

desk verdict Solid, clearly-written forecast that makes a real subfield contribution; the low-mass halo constraints lean on a cluster-calibrated miscentering prior that the paper itself flags, but the galaxy-based path is independent and the central claim holds. read the letter →

arxiv 1909.00405 v2 pith:Y5EB7DCA submitted 2019-09-01 astro-ph.CO astro-ph.GA

S. Pandey , E.J. Baxter , J.C. Hill This is my paper · ORCID

classification astro-ph.COastro-ph.GA

keywords thermalSunyaev-Zel'dovicheffectCompton-yparameterhalopressureprofilesbaryonicfeedbackgalaxy-ycross-correlationmodelcosmologyforecastsDESIandCMB-S4

topics Dark Matter

open problems Dark Matter

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper forecasts that cross-correlating future galaxy and halo catalogs with maps of the thermal Sunyaev-Zel'dovich effect will measure the gas pressure around dark matter halos precisely enough to discriminate between competing feedback models. The authors model halo-y and galaxy-y correlations in the halo model, adopting a parameterized pressure profile with free amplitude and shape, and include observational systematics such as halo miscentering and mass bias. For a DESI-like sample and CMB-S4-like Compton-y maps, the projected signal-to-noise reaches roughly 510 $\sigma$ for the most massive halos and about 40 $\sigma$ for halos near $10^{12}$ solar masses, and the inferred 3D pressure profiles are tight enough to confirm or rule out current feedback prescriptions. The paper argues that the y auto-spectrum alone cannot constrain low-mass halos, so the cross-correlations are the key probe.

What carries the argument

The load-bearing object is the parameterized halo pressure profile $P_e(x|M,z)$, written as a generalized Navarro-Frenk-White form with amplitude $P_0$, shape $\beta$, and a set of mass-scaling indices, with additional low-mass freedom added for the galaxy-based forecasts. Fourier-transformed into multipole-space profiles and combined with the halo model's one- and two-halo terms, this profile predicts the halo-y and galaxy-y cross-spectra. The other essential pieces are the miscentering model (a Rayleigh-distributed offset convolved into the real-space profile) and a lognormal mass-bias distribution with a 10 percent prior, which capture the systematics that otherwise bias the inferred pressure profiles.

What would settle it

Measure the stacked tSZ profile around DESI-identified groups with measured masses near $10^{12}$–$10^{13}$ solar masses using a CMB-S4-like y map, and compare the recovered amplitude and shape of the pressure profile with the forecast 2-$\sigma$ bands; the claim would be falsified if the actual error bars are much larger, or if the small-scale profile is suppressed far more than the assumed 22 percent miscentered fraction predicts.

Watch

Extended reading notes

Core claim

On its own terms, the paper claims that upcoming measurements of the two-point cross-correlation between dark matter halos (or galaxies) and Compton-y maps will turn the tSZ effect into a precision probe of baryon physics in group-scale halos. Treating the pressure profile as a generalized NFW form with free amplitude P0 and shape beta, and marginalizing over miscentering and mass-bias systematics, the forecasts show 2-sigma uncertainty bands on the 3D pressure profiles that are narrow enough to separate the feedback models realized in current hydrodynamical simulations. The projected constraints on the integrated Y-M relation from halo-y correlations and galaxy-y correlations are far tighter than those from the y auto-spectrum at low halo mass, enabling a direct test of whether AGN and supernova feedback prescriptions capture the thermodynamic state of the gas.

Load-bearing premise

The load-bearing assumption is that the miscentering parameters measured for massive optically selected clusters (a typical offset scale and a 22 percent miscentered fraction) apply unchanged to halos as light as $10^{12}$ solar masses.

Editorial extensions

If this is right

DESI-like halo samples correlated with CMB-S4-like y maps should detect the one-halo tSZ signal at roughly 40, 210, and 510 sigma in the mass bins $10^{12}$–$10^{13}$, $10^{13}$–$10^{14}$, and $10^{14}$–$10^{15}$ solar masses per $h$, at $z$ between 0.2 and 0.3.
Pressure-profile constraints from halo-y correlations are good enough to distinguish the feedback models in current hydrodynamical simulations, including on the integrated $\tilde{Y}$-$M$ relation.
The Compton-y auto-spectrum alone gives much weaker constraints on low-mass halos, so galaxy and halo cross-correlations are necessary to probe group-scale gas.
At high halo mass, the halo-y data can self-calibrate the miscentering parameters, while at low mass the assumed miscentering prior matters more than mass calibration.
Halo-y pressure constraints are only weakly degenerate with $\sigma_8$, unlike the y auto-spectrum, so they remain informative even when cosmology is left free.

Reading between the lines

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

A natural extension is to split the galaxy sample by color or star-formation activity at fixed halo mass; the same measurement would then test whether red galaxies show more extended or hotter gas, as feedback quenching scenarios predict.
Combining these tSZ cross-correlations with kinematic SZ measurements around the same halos could separate thermal from non-thermal pressure support, a quantity feedback models predict but current tSZ data alone cannot measure.
If the miscentering extrapolation to low-mass halos is wrong, the forecast degradation suggests that investing in better group centering (e.g., from deep imaging or weak-lensing peak positions) may be as valuable as deeper CMB maps for the low-mass science case.
The same HOD-based pipeline applied to photometric samples like LSST should work without the need for a group catalog, since the modeling marginalizes over the galaxy-halo connection.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is one of the better forecast papers I have seen in this area. It takes a standard halo-model pipeline, makes the systematics explicit, and gives numbers that will be useful for planning DESI/SO/CMB-S4 cross-correlations. The genuinely new pieces are the piecewise low-mass pressure profile extension (Eq. 10), the combined miscentering and mass-bias treatment, and the survey-specific forecasts. It is honest about what a self-consistency forecast can and cannot say.

What the paper does well: the model equations are standard and clearly presented, the priors are tabulated, and the covariance treatment follows the literature. The comparison against y-autospectrum-only constraints makes a strong case that halo- and galaxy-y correlations are the route to low-mass pressure profiles. The galaxy-based forecasts marginalize over HOD parameters and still show discriminating power between feedback models, which is a stronger result than I expected. Credit where it is due.

Soft spots, in order. First, the forecast is self-consistency by construction: mock data generated from the fiducial model are fit with the same model, so the tight bands in Figures 3, 6, and 9 should be read as upper limits on constraining power, not predictions that the real sky will cooperate. That is standard for forecast papers, but worth saying plainly. Second, the stress-test concern about miscentering lands. The Rykoff et al. cluster constraints are extrapolated to 1e12 Msun halos, and for the lowest mass bin the fmis posterior is prior-dominated. If group-scale centering is worse than assumed, the low-mass pressure-profile bands will widen. The authors state this assumption explicitly, so I do not call it hidden; I call it the weakest load-bearing assumption in the halo-based half of the paper. Third, non-Gaussian covariance for halo-involving spectra is set to zero with no quantified impact, which could make the error bars optimistic at high ell. Fourth, the CIB and completeness assumptions are acknowledged and are probably fine at low z.

The math is standard, the citation pattern is appropriate, and no code is shipped, but the parameter tables and survey noise prescriptions are detailed enough to reproduce the essentials. Net: the paper deserves serious refereeing. The central qualitative conclusion, that upcoming surveys can turn y cross-correlations into real feedback constraints, is well supported within the model framework. I would send it out.

Referee Report

3 major / 4 minor

Summary. This paper forecasts how well future galaxy and halo samples (DESI-like and LSST-like) cross-correlated with Simons Observatory and CMB-S4 Compton-y maps will constrain the pressure profiles of dark matter halos. The authors use the halo model with one- and two-halo terms, a generalized NFW pressure profile based on Battaglia et al. (2012) with additional low-mass freedom, Gaussian plus non-Gaussian covariance, and parameterized systematics for halo miscentering and mass bias. They report projected signal-to-noise of roughly 40, 210, and 510 sigma for halo mass bins 10^12-10^13, 10^13-10^14, and 10^14-10^15 Msun/h, forecast tight 3D pressure profile constraints, and argue that the resulting Y-M relation constraints can distinguish feedback prescriptions such as AGN8/AGN8.5 from the shock-heating model.

Significance. If the forecasts hold, this work makes a strong case that small-beam CMB surveys combined with DESI/LSST galaxy samples will transform tSZ cross-correlations from detections into precision measurements of group-scale baryon physics, with direct consequences for feedback modeling and for the control of baryonic systematics in weak lensing. The analysis is careful in several respects: the parameterized treatment of miscentering and mass bias, the realistic SO/CMB-S4 noise curves including atmospheric noise and ILC residuals, and the comparison against independent hydrodynamical feedback predictions. The main caveats are that the forecasts are self-consistency forecasts in which mock data are generated with the fiducial model and fit with the same model, and that several simplifying assumptions with potentially large impact are not quantified.

major comments (3)

[§II.D.1, §III.B, Fig. 5] The low-mass pressure-profile constraints that underpin the central claim are purchased with a cluster-calibrated miscentering prior that is explicitly extrapolated to group-scale halos: the text states that the Rykoff et al. (2016) constraints 'effectively extrapolate' to low halo masses. Since §III.B notes that for low-mass halos the miscentering-fraction prior matters more than mass calibration, and Fig. 5 shows prior-dominated fmis constraints in the low-mass bins, the tightness of the blue bands in Fig. 3 and the feedback-discrimination power in Fig. 6 depend on this unvalidated assumption. I request sensitivity tests with e.g. fmis ~ 0.5 and/or a wider ln cmis prior, and that the low-mass claims be restated as conditional on the assumed group-scale miscentering distribution.
[§II.C, Eq. (22)] The non-Gaussian covariance is set exactly to zero for all halo-involving spectra on the grounds that 'the one-halo term should not contribute to the trispectrum of correlations involving halos.' This is asserted rather than demonstrated, and a naive halo-model treatment of discrete halos would seem to produce a Poisson-type contribution (e.g. proportional to the integral of dn/dM times the squared y-profile for the halo-y covariance) that is not included in the Gaussian term. Because the headline signal-to-noise values and the parameter-error forecasts in Figs. 3-6 are computed with this covariance, the impact of the omitted term should be quantified, or a derivation/citation should be supplied if the term is genuinely absent.
[§II.E.2] The halo-based forecasts assume unity completeness for the halo catalog. For the lowest mass bin, 10^12-10^13 Msun/h, this is optimistic relative to existing group catalogs, and the paper itself notes that Yang et al. (2007) achieved only about 85% completeness above 10^12 Msun/h. Mass-dependent incompleteness would both enlarge the errors and bias the recovered pressure profiles. A sensitivity test at plausible completeness levels, or a discussion of how incompleteness would propagate into the Fig. 3 constraints, would strengthen the forecasts.

minor comments (4)

[§II.B] 'Viral mass' should read 'virial mass' in the sentence describing the relation between r_s and r_vir.
[§II.D.3, Fig. 3] The assumption that CIB contamination can be controlled below statistical errors is an important caveat for the high-redshift bin (0.9 < z < 1.2) in Fig. 3, where the authors acknowledge CIB is more problematic; a quantitative estimate of the residual CIB bias would help the reader assess the high-redshift constraints.
[References] The reference labeled 'Planck Collaboration et al., 2016a' appears malformed (it contains '] 10.1051 /0004-6361/201629022' in place of a complete citation) and should be corrected.
[Figs. 6 and 9] The y-axis labels use the ratio ilde Y500/(M500/10^15 h^-1 Msun)^5/3; defining ilde Y once in the caption or text, as is done in Eq. (33), would make the figures easier to interpret without cross-referencing.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the forecast uses standard halo-model signal and covariance inputs, with pressure-profile, feedback, miscentering, and mass-calibration inputs drawn from independent external work.

full rationale

The paper's derivation chain is a standard forecast: it computes halo-y and galaxy-y power spectra from a halo-model formalism (Tinker mass function and bias, Battaglia et al. 2012 pressure profile), assigns covariance from Gaussian and one-halo trispectrum terms plus external survey noise curves (SO, CMB-S4), and then fits the same model to mock data vectors generated from the fiducial model. This is a self-consistency forecast, not a circular derivation: the tightness of the projected constraints is controlled by the covariance and by parameter degeneracies, not by construction, and the paper does not claim an external measurement. The feedback-model discrimination in Figs. 6 and 9 uses predictions from Le Brun et al. (2015) hydrodynamical simulations, which are independent external benchmarks and are not self-citations. The miscentering priors come from Rykoff et al. (2016) and the mass-bias prior from external weak-lensing calibration estimates; the paper explicitly flags the low-mass miscentering extrapolation as an assumption. That is a limitation or correctness risk, not circularity. Self-citations to prior work (Hill et al. 2018, Pandey et al. 2019) are contextual and not load-bearing. No quoted equation or parameter is defined in terms of the target result, and no fitted quantity is renamed as a prediction.

Assumptions & free parameters 14 free parameters · 10 assumptions · 0 invented entities

No new physical entities are introduced; Eq. 10 is a parameterization extension, not new physics. The free parameters listed are the varied model parameters with fiducial values from prior literature or chosen by hand; the forecasted constraints depend on these fiducial choices.

free parameters (14)

P0 = 18.1
Fiducial amplitude of the generalized NFW pressure profile (Eq. 7), taken from Battaglia et al. (2012) and varied in forecasts (Tables I and II).
beta = 4.35
Outer slope of the pressure profile; fiducial from Battaglia et al. (2012), varied in forecasts.
alpha_p,high = 0.154
Mass scaling index for P0 at high mass (Eq. 9), fiducial from Battaglia et al. (2012); varied in galaxy-based forecasts.
alpha_p,mid = 0.0
Low-mass pressure scaling index introduced in this work (Eq. 10) to allow feedback effects at intermediate mass; fiducial set to 0, varied in galaxy-based forecasts.
alpha_p,low = 0.0
Additional low-mass pressure scaling index introduced in this work (Eq. 10); varied in galaxy-based forecasts.
log M0 = 12.23
Minimum halo mass for satellite galaxies in the HOD (Eq. 14), fiducial from Zehavi et al. (2011); varied in galaxy-based forecasts.
log M1 = 12.75
Pivot mass of the satellite occupation relation (Eq. 14), fiducial from Zehavi et al. (2011); varied.
alpha_g = 0.99
Power law index of the satellite occupation relation (Eq. 14), fiducial from Zehavi et al. (2011); varied.
ln cmis = -1.1
Miscentering offset scale relative to virial radius (Eq. 26), fiducial from Rykoff et al. (2016); prior width 0.2 in halo-based forecasts.
fmis = 0.2
Fraction of miscentered halos (Eq. 28), fiducial from Rykoff et al. (2016); prior width 0.1.
eta = 1.0
Halo mass bias parameter (Eq. 30), fiducial 1.0 with 10% Gaussian prior in halo-based forecasts.
Mhigh = 3e14 Msun/h
Pivot mass for the pressure scaling (Eq. 9), chosen from Le Brun et al. (2015); fixed, not marginalized.
Mlow = 3e13 Msun/h
Pivot mass for low-mass pressure modifications (Eq. 10), chosen by hand in this work; fixed, not marginalized.
sigma_lnM = 0.5
Scatter in the mass-observable relation (Eq. 29), fixed by hand as a reasonable level.

assumptions (10)

domain assumption The Battaglia et al. (2012) AGN-200c generalized NFW pressure profile is an adequate template for halo gas pressure across 1e12-1e15 Msun/h, with only amplitude and outer slope free.
Introduced in Sec. II A; extrapolates a fit calibrated at M > 5e13 Msun/h to group-scale halos.
standard math Tinker et al. (2008, 2010) fitting functions for the halo mass function and linear bias are accurate.
Used in Eqs. 1, 2, and 6; standard in the literature.
domain assumption Electron pressure relates to total pressure via the primordial helium mass fraction Y according to Eq. 4.
Sec. II A, Eq. 4; assumes fully ionized hydrogen and helium gas.
domain assumption Covariance can be modeled as Gaussian plus one-halo trispectrum, with the non-Gaussian term set to zero for correlations involving halos.
Sec. II C, after Eq. 23; approximation stated without quantitative impact estimate.
domain assumption Galaxy and halo catalogs are complete within the chosen mass and redshift bins.
Sec. II E 2; completeness fraction assumed unity.
domain assumption CIB contamination of the y maps can be controlled below statistical errors.
Sec. II D 3; assumption stated, with detailed modeling deferred to future work.
ad hoc to paper Rykoff et al. (2016) miscentering constraints for galaxy clusters apply to all halo masses down to 1e12 Msun/h.
Sec. II D 1; explicit extrapolation flagged by the authors.
domain assumption Halo masses can be calibrated to 10% precision via weak lensing or other methods.
Sec. II D 2; assumed conservative prior on eta.
domain assumption HOD parameters from the SDSS volume-limited sample (Zehavi et al. 2011) describe the DESI BGS sample.
Sec. II E 3; fiducial values adopted from SDSS with justification by similar absolute magnitude limit.
standard math Flat LCDM with Planck 2018 best-fit parameters is the underlying cosmology.
Sec. I end; cosmology fixed except in Sec. III D where sigma8 is varied.

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Cite this review

Pith. "Pith review of Constraining the properties of gaseous halos via cross-correlations of upcoming galaxy surveys and thermal Sunyaev-Zel'dovich maps." pith.science (2026). https://pith.science/paper/Y5EB7DCA

@misc{pith2026190900405,
  author       = {Pith},
  title        = {Pith review of: Constraining the properties of gaseous halos via cross-correlations of upcoming galaxy surveys and thermal Sunyaev-Zel'dovich maps},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Y5EB7DCA}},
  note         = {Machine review of arXiv:1909.00405}
}

abstract

The thermal Sunyaev-Zel'dovich (tSZ) effect induces a Compton-$y$ distortion in cosmic microwave background (CMB) temperature maps that is sensitive to a line of sight integral of the ionized gas pressure. By correlating the positions of galaxies with maps of the Compton-$y$ distortion, one can probe baryonic feedback processes and study the thermodynamic properties of a significant fraction of the gas in the Universe. Using a model fitting approach, we forecast how well future galaxy and CMB surveys will be able to measure these correlations, and show that powerful constraints on halo pressure profiles can be obtained. Our forecasts are focused on correlations between galaxies and halos identified by the upcoming Dark Energy Spectroscopic Instrument survey and tSZ maps from the Simons Observatory and CMB-S4 experiments, but have general applicability to other surveys, such as the Large Synoptic Survey Telescope. We include prescriptions for observational systematics, such as halo miscentering and halo mass bias, demonstrating several important degeneracies with pressure profile parameters. Assuming modest priors on these systematics, we find that measurements of halo-$y$ and galaxy-$y$ correlations with future surveys will yield tight constraints on the pressure profiles of group-scale dark matter halos, and enable current feedback models to either be confirmed or ruled out.

Figures

Figures reproduced from arXiv: 1909.00405 by the authors.

**Figure 2.** , shows the model halo-y spectra, including the one and two-halo components, for three different mass bins and for the redshift bin 0.2 < z < 0.3. Also shown are the forecasted errorbars for a CMB-S4-like experiment. The projected total signal-to-noise for each of the mass bins is high, roughly 40σ for halos in the bin [1012 , 1013]M /h, 210σ for [1013 , 1014]M /h, and 510σ for [1014 , 1015]M /h. The one halo term … view at source ↗

**Figure 3.** shows the constraints on the 3D pressure profiles for three halo mass bins and two redshift bins, as inferred from the forecasted halo-y correlation measurements. We have generated these forecasts while varying the parameters shown in Table I (with the priors described therein) for each halo mass [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (8 more)

**Figure 4.** Figure 4: compares the pressure profile constraints on lowmass halos that can be obtained from SO to those projected for CMB-S4. Both experiments provide similar constraints on the pressure profiles of low mass halos, given their substantial improvement in beam size and map de…

**Figure 5.** Figure 5: FIG. 5. Constraints on the pressure profile and systematics parameters (Table I) obtained from analyzing the halo- [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

**Figure 6.** Figure 6: additionally shows the forecasted constraints on the Y˜-M relation from the analysis of the y autospectrum (red bands). The y autospectrum is mostly sensitive to halos with M > 1013 M , with some dependence on redshift and `. Consequently, at low mass, the y autospect…

**Figure 7.** Figure 7: FIG. 7. The impact of allowing freedom in [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

**Figure 8.** Figure 8: At high mass and for a narrow bin, at high [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]

**Figure 8.** Figure 8: FIG. 8. The dependence of [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]

**Figure 9.** Figure 9: FIG. 9. The 2- [PITH_FULL_IMAGE:figures/full_fig_p016_9.png]

**Figure 10.** Figure 10: FIG. 10. Constraints on model parameters from joint fits to the galaxy- [PITH_FULL_IMAGE:figures/full_fig_p017_10.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

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

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In this process, some assumptions must be made about the centers of these halos [e.g

Miscentering Our halo-based forecasts assume that the galaxy distribu- tion has been used to identify the locations of halos. In this process, some assumptions must be made about the centers of these halos [e.g. 72]. Frequently, the halo center is chosen to be at the location of the brightest galaxy in the identiﬁed halo. However, this prescription may no...

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Mass bias For the halo-based forecasts, we assume that the halo popu- lation can be divided into bins based on halo mass. Of course, inferring halo masses is challenging, and may be subject to systematic errors; we refer to any diﬀerence between the true halo mass and the assumed halo mass as mass bias. Perhaps the most powerful way to infer halo masses i...

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Of these, the CIB is potentially the most problematic, as shown in e.g

Biases in the y maps Another potential source of systematic error for the halo- y correlation measurements is contamination of the Compton- y maps by other sources of mm-wave emission, such as the cosmic infrared background (CIB) and radio point sources [56]. Of these, the CIB is potentially the most problematic, as shown in e.g. Pandey et al. [51], since...

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Battaglia N., Bond J. R., Pfrommer C., Sievers J. L., Sijacki D., 2010, ApJ, 725, 91

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CMB surveys We focus on the future CMB-S4 survey [2] and also present some results for the imminent Simons Observatory (SO) sur- vey [3] in this work, although ongoing ground-based CMB surveys (e.g., Advanced ACT [31] and SPT-3G [12]) should also produce high-precision tSZ cross-correlation measure- ments in the near term. The speciﬁcations of the SO and ...

2022

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The ﬁrst assumes that the galaxy survey is used to identify an underlying population of dark matter halos

Galaxy survey: halos For the galaxy survey, we consider two types of forecasts. The ﬁrst assumes that the galaxy survey is used to identify an underlying population of dark matter halos. The second type 1 https://simonsobservatory.org/assets/supplements/ 20180822_SO_Noise_Public.tgz 8 assumes that the galaxy-y correlation is measured directly, and a HOD i...

work page

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We adopt the HOD model described in §II B

Galaxy survey: galaxies Our galaxy-based forecast is designed to represent the BGS sample of DESI [21]. We adopt the HOD model described in §II B. We choose the ﬁducial values of the HOD parame- ters to be equal to the best ﬁt values for sub-sample of SDSS redshift survey galaxies having absolute magnitude less than -19.5 [73] since BGS galaxies are expec...

work page

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Battaglia N., et al., 2019, in Bulletin of the American Astro- nomical Society. p. 297 (arXiv:1903.04647)

arXiv 2019