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Missing baryons recovered: a measurement of the gas fraction in galaxies and groups with the kinematic Sunyaev-Zel'dovich effect and CMB lensing

T0 review · 1 major / 1 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Stacking CMB lensing from ACT DR6 around DESI galaxies calibrates halo masses and, combined with kSZ gas profiles, shows that the baryon fraction reaches the cosmic value at 2-3 virial radii while dropping to about 0.3 in group centers.

desk verdict A careful, well-validated lensing mass calibration for DESI samples with a novel kSZ comparison, but the headline gas-fraction numbers lean on an HOD-extrapolated matter profile at small radii; the qualitative result is likely right, the significance is not. read the letter →

arxiv 2507.14136 v1 pith:EHJTTQLY submitted 2025-07-18 astro-ph.CO

Boryana Hadzhiyska , Simone Ferraro , Gerrit S. Farren , Noah Sailer , Rongpu Zhou This is my paper
classification astro-ph.CO
keywords kinematicSunyaev-Zel'dovicheffectCMBlensingbaryonfractionmissingbaryonshalooccupationdistributionbaryonicfeedbackgalaxygroupsDESI
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

Using CMB lensing maps from ACT DR6 stacked around DESI galaxies, this paper calibrates the average halo masses and total matter profiles of three galaxy samples, then compares those profiles with gas profiles previously measured through the kinematic Sunyaev-Zel'dovich (kSZ) effect. The comparison is nearly parameter-free because the lensing measurement supplies the halo mass that earlier kSZ analyses had to assume. The paper finds that at radii of roughly 2-3 virial radii the kSZ gas profile matches the lensing total-matter profile, so the cumulative gas fraction approaches the cosmic baryon fraction and the 'missing baryons' appear to be present in the outskirts. At small radii the gas fraction drops to about 0.3 of the cosmic value, a deficit the paper attributes to baryonic feedback that pushes gas out of group centers. Contrasting these fractions with the TNG300 simulation, which predicts systematically higher gas fractions at fixed radius, the paper concludes that feedback in the real Universe must be stronger than in that simulation.

What carries the argument

The machinery is the ratio of two projected profiles for identical galaxy samples: the kSZ gas profile (from reference [13]) and the total matter profile obtained by converting the ACT DR6 CMB lensing convergence $\kappa(\theta)$ into a galaxy-matter cross-spectrum $P_{gm}(k,z)$ via a five-parameter halo occupation distribution (HOD) model, a description of how many central and satellite galaxies populate halos of a given mass, calibrated on AbacusSummit N-body simulations. The HOD gives the mean halo mass and satellite fraction, and the lensing-derived matter profile is converted into the same compensated-aperture-photometry (CAP) units as the kSZ signal, so the comparison requires no free amplitude. The central ratio is $f_{\rm gas}(<R)/(\Omega_b/\Omega_m)$, the cumulative gas fraction normalized to the cosmic baryon fraction, corrected for the CMB beam with a simulation-calibrated transfer function.

What would settle it

Measure the velocity reconstruction cross-correlation coefficient $r$ directly from DESI spectroscopy for the same LRG samples; if the true $r$ is high enough to raise the kSZ gas profiles by roughly 30 percent at small radii, the claimed $6.5\sigma$ gas/matter discrepancy and the $>4\sigma$ TNG300 disagreement would both shrink below significance. Alternatively, an X-ray or thermal-SZ measurement finding $f_{\rm gas}(R_{200m})/(\Omega_b/\Omega_m)\approx 0.85$ rather than $\approx 0.3$ for these halos would falsify the baryon depletion claim.

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Extended reading notes

Core claim

The central claim is that the combination of CMB lensing and kSZ measurements around the same DESI galaxy samples yields a direct, largely assumption-free measurement of the gas-to-total-mass ratio as a function of radius, and that this ratio indicates a complete baryon budget at large radii and strong baryon depletion inside halos. Concretely, the authors report mean halo masses $\log(M_{\rm halo}/(M_\odot/h)) \approx 13.18$, $13.03$, and $13.02$ for Main LRGs, Extended LRGs, and BGS; agreement between gas and matter profiles at $\sim 2$-$3$ Mpc$/h$ (a few virial radii) implying full baryon recovery; a $\sim 6.5\sigma$ shortfall of gas relative to matter at small apertures; and gas fractions at the virial radius of $\sim 0.3$ of the cosmic baryon fraction, matching X-ray-based relations. Compared with the TNG300 hydrodynamical simulation, the observed gas fractions are lower by $\gtrsim 4\sigma$ at fixed radius, which the authors interpret as evidence for stronger baryonic feedback in the real Universe.

Load-bearing premise

The gas fraction measurement depends on the five-parameter HOD model converting the CMB lensing convergence into the correct total matter profile in kSZ units, and that model is evaluated at a single snapshot redshift with no assembly bias or redshift evolution; if this conversion is wrong, the inferred gas fraction and the feedback discrepancy would be biased.

Editorial extensions

If this is right

  • The mean halo masses of DESI Main LRGs, Extended LRGs, and BGS are now calibrated by lensing at $\log(M_{\rm halo}/(M_\odot/h)) \approx 13.18$, $13.03$, and $13.02$, respectively, providing an external anchor for kSZ and clustering analyses.
  • At radii of 2-3 virial radii, the cumulative gas fraction reaches the cosmic baryon fraction, meaning the historically 'missing' baryons are present in group outskirts rather than absent from the Universe.
  • Inside roughly 1 arcmin, only about 30 percent of the cosmic baryon fraction remains in the gas phase, requiring feedback processes that expel gas from halo centers.
  • The TNG300 simulation's gas fractions exceed the observed ones by more than $4\sigma$ at fixed radius, indicating that real feedback is stronger than in that simulation.
  • The kSZ-derived gas fraction at the virial radius agrees with X-ray-based empirical relations, supporting a consistent picture across independent probes.

Reading between the lines

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

  • A natural extension is to repeat this analysis on DESI spectroscopic samples with the same ACT maps; if the small-scale gas/matter discrepancy shrinks once assembly bias or redshift evolution is added to the HOD, the current $6.5\sigma$ signal would need to be reinterpreted as partly a modeling artifact.
  • Upcoming CMB lensing maps from Simons Observatory and CMB-S4 will lower the lensing noise enough to make the gas/matter ratio a sharper probe of feedback, potentially measuring the gas fraction profile per stellar mass bin rather than for broad samples.
  • The large-radius baryon recovery implies that the 'missing baryons' problem is largely a question of where observers look, but the paper does not establish whether the recovered gas is bound to the halos or simply part of the surrounding large-scale structure.
  • A fully joint fit of kSZ and lensing data inside one halo model, rather than comparing separately measured profiles, would place the feedback constraint on a single likelihood and reduce sensitivity to the velocity reconstruction coefficient.
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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

1 major / 1 minor

Summary. The paper measures the mean halo masses and projected matter density profiles of three DESI photometric samples (Main LRG, Extended LRG, and BGS) by stacking the public ACT DR6 CMB lensing convergence map, and interprets the measurements with a five-parameter HOD model emulated from AbacusSummit. Using the best-fit HOD, the authors convert the lensing-derived matter profile into kSZ-like units and compare it with the gas profiles measured by Hadzhiyska et al. (2024). They report that the gas and matter profiles agree at 2-3 virial radii, recovering the cosmic baryon fraction, while at small radii the gas fraction falls to ~0.3, inferring strong baryonic feedback. They also find that TNG300 overpredicts the gas fraction by about 4 sigma relative to the observations.

Significance. If the result holds, the paper would provide an independent CMB-lensing calibration of halo masses for DESI samples and a scale-dependent gas-to-matter ratio that directly tests baryonic feedback models. The analysis is carefully validated in several respects: end-to-end mocks through the ACT DR6 lensing reconstruction pipeline, foreground contamination tests with WebSky and the CIB-deprojected map, and an emulator with reported RMSE ~1e-4 and R^2 ~0.9998. These strengths make the halo-mass calibration credible. However, the headline gas-fraction results rely on the shape of the matter profile extrapolated from the HOD at scales not directly probed by the band-limited lensing map, so the feedback conclusion is less secure than the mass calibration.

major comments (1)
  1. [Section IV.B; Eq. (15); Section II.B] The TNG300 comparison in Section IV.B and Fig. 6 is described as using a 'Main-like sample', but the matching between the observed LRG sample and the simulated galaxies is not fully specified (e.g., whether the simulated galaxies are selected by stellar mass with the same scatter, whether the redshift distributions match, and whether the simulated profiles are evaluated at the same lens redshifts as the DESI data). Since the gas fraction is a ratio and the paper emphasizes that the comparison is 'relative rather than absolute', the matching details are needed to assess the 4 sigma offset.
minor comments (1)
  1. [Section IV.B] The paper uses 'LRGs' both as a sample name and as a generic galaxy class; the Extended sample selection (Section II.A) should be restated at first use in Section IV.B to avoid ambiguity.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the kSZ gas profile and the CMB lensing mass calibration are independent observables, and the self-cited r coefficient is an external simulation-based calibration, not a fitted target.

full rationale

The paper's central derived quantity, the gas fraction f_gas(<R) = (kSZ gas profile)/(lensing-based matter profile), is a ratio of two independent measurements. The numerator comes from the previously published kSZ stack of Hadzhiyska et al. (2024), while the denominator comes from a five-parameter HOD fit to the ACT DR6 CMB lensing convergence profile alone. The kSZ signal is not used in the HOD likelihood (Eq. 12), so the comparison is not self-referential: a mis-specified HOD or a different gas profile would change the ratio, and the data are free to disagree with the model, as they do at small radii (6.5 sigma discrepancy) and with TNG300 (4 sigma offset). The one input inherited from the authors' prior work is the velocity cross-correlation coefficient r (r=0.3 Main, r=0.25 Extended), which scales the gas profile amplitude. However, r is not fitted to the target data; it is calibrated in separate simulation-based studies [40,41] that are externally falsifiable (e.g., by the future spectroscopic determination the paper explicitly defers to). The paper transparently quotes a 10-15% systematic from velocity reconstruction, so no fitted parameter is renamed as a prediction. The small-scale matter profile is an HOD extrapolation beyond the ACT L<3000 filter, creating model dependence in the denominator, but the paper explicitly argues this step could be replaced by a spline extension of the smooth C^{kappa g}_ell, and validates it in simulations; this is a robustness limitation, not a logical reduction of the result to its inputs. No equation defines a target quantity in terms of itself, and no load-bearing claim rests on an unverified self-citation chain. The paper is self-contained against external benchmarks (ACT DR6 map, AbacusSummit, TNG300, eROSITA comparisons), so the appropriate finding is no significant circularity.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the HOD model and the velocity reconstruction calibration, both of which are external inputs adopted from prior work rather than derived here.

free parameters (2)
  • HOD parameters (5 per sample) = Main: logMc=12.683, logM1=14.063, sigma=0.133, alpha=0.848, kappa=1.245; Ext: 12.491, 14.196, 0.108, 0.642, 0.941…
    Fitted to the ACT DR6 lensing profiles; they determine the matter profile and mean halo mass.
  • velocity cross-correlation coefficient r = 0.3 (Main), 0.25 (Extended)
    Adopted from prior work by the same group; directly scales the kSZ gas profile amplitude and gas fraction.
assumptions (5)
  • domain assumption Gas is fully ionized with primordial abundances (XH=0.76) at the scales probed by kSZ.
    Equation 9 in Section III.E; underpins the conversion from kSZ temperature to gas density. If the gas is not fully ionized or has non-primordial abundances, the inferred gas fraction would be underestimated.
  • domain assumption The vanilla five-parameter HOD model accurately describes the galaxy-halo connection for the LRG and BGS samples.
    Section III.B; the model is used to compute the galaxy-matter power spectrum and to convert the lensing signal into a matter density profile. The paper acknowledges the fit is poor for BGS.
  • domain assumption The ACT DR6 lensing reconstruction is unbiased for these samples; residual foreground bias is below 5 percent.
    Section III.D; validated with mock lensed CMB maps and WebSky foregrounds. The 5 percent systematic is an input choice.
  • domain assumption The velocity reconstruction cross-correlation coefficient r is correct for the DESI photometric samples.
    Section II.D; r is taken from Hadzhiyska et al. 2024 and affects the kSZ amplitude by 10-15 percent.
  • domain assumption The lensing signal is dominated by the halo one-halo term on the scales used for the mass profile; two-halo and baryonic effects are negligible or correctly forward-modeled.
    Section III.C and IV.A; the L<3000 filter reduces small-scale sensitivity, and baryonic effects on lensing are argued to be small.

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Cite this review

Pith. "Pith review of Missing baryons recovered: a measurement of the gas fraction in galaxies and groups with the kinematic Sunyaev-Zel'dovich effect and CMB lensing." pith.science (2026). https://pith.science/paper/EHJTTQLY

@misc{pith2026250714136,
  author       = {Pith},
  title        = {Pith review of: Missing baryons recovered: a measurement of the gas fraction in galaxies and groups with the kinematic Sunyaev-Zel'dovich effect and CMB lensing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EHJTTQLY}},
  note         = {Machine review of arXiv:2507.14136}
}
abstract

We present new constraints on the halo masses and matter density profiles of DESI galaxy groups by cross-correlating samples of Luminous Red Galaxies (LRGs) and Bright Galaxy Survey (BGS) galaxies with the publicly available CMB lensing convergence map from ACT DR6. This provides an independent, lensing-based calibration of halo masses, complementary to methods relying on clustering or dynamics. We derive constraints on the mean halo mass for three DESI-selected samples, finding $\log(M_{\rm halo}/(M_\odot/h)) \approx 13.18$, 13.03 and 13.02 for the Main LRG, Extended LRG, and BGS samples, respectively. Using a halo model approach, we also compare the projected galaxy-matter density profiles with previously reported gas profiles inferred from measurements of the kinematic Sunyaev-Zel'dovich (kSZ) effect. This work addresses one of the key uncertainties in interpreting kSZ signals -- the unknown host halo mass distribution -- by providing an independent and consistent mass calibration. The agreement between the gas and total mass profiles at large aperture suggests that sufficiently far from the group center (2--3 virial radii), we recover all the baryons, offering a resolution to the 'missing baryon' problem. We further study the cumulative gas fractions for all galaxies as well as for the most massive galaxy groups in the sample ($\log(M_{\rm halo}/(M_\odot/h)) \approx 13.5$), finding values that are physically sensible and in agreement with previous findings using kSZ and X-ray data: compared to the TNG300 simulation, the observed gas fractions are systematically lower at fixed radius by $\gtrsim$4$\sigma$, providing compelling, independent evidence for stronger baryonic feedback in the real Universe. These findings highlight the power of combining CMB lensing with galaxy surveys to probe the interplay between baryons and dark matter in group-sized halos.

Figures

Figures reproduced from arXiv: 2507.14136 by the authors.

Figure 2
Figure 2. FIG. 2. Lensing convergence [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Correlation matrix of the lensing signal [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Scatter plot comparing the kSZ amplitude at the third radial [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figures from the paper (8 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison between the gas density profile measured from [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: shows the inferred baryon fraction 𝑓gas(< 𝑅)/(Ωb/Ωm) as a function of aperture radius for both the Main and Extended LRG samples, where Ωb/Ωm is the cos￾mic baryon fraction. This ratio is computed by dividing the gas density profile derived from the kSZ signal [13] by …
Figure 7
Figure 7. Figure 7: FIG. 7. CAP profiles in kSZ units for gas (solid lines) and dark matter [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Stellar-halo mass relation for the Extended LRG samples [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Redshift evolution of the lensing signal [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]

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Forward citations

Cited by 9 Pith papers

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    Non-linear velocity terms cancel in real-space linear reconstruction, but redshift-space distortions reintroduce a 10–20% small-scale suppression of the stacked kSZ signal.

  4. Measurement of the galaxy-velocity power spectrum of DESI tracers with the kinematic Sunyaev-Zeldovich effect using DESI DR2 and ACT DR6

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    DESI DR2 and ACT DR6 data yield 17σ LRG-velocity, 8.3σ ELG-velocity, and 6.8σ QSO-velocity detections plus a 3.1σ velocity-velocity signal, producing f_NL^loc = 15.9_{-34.4}^{+34.6} from the velocity field.

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