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Interpreting the stacked kinetic SZ effect I: velocity reconstruction and non-linear velocity effects

T0 review · 2 major / 4 minor · reviewed 2026-07-31 · deepseek-v4-flash

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Pith's one-line read Velocity errors bias stacked kinetic-SZ signal by 10-20 percent

desk verdict Useful simulation-based result: RSD in velocity reconstruction creates a ~10% scale-dependent kSZ suppression, nearly baryon-independent, but the satellite-FoG attribution depends on an unverified stripping assumption. read the letter →

arxiv 2607.23339 v1 pith:XVJOOTIH submitted 2026-07-25 astro-ph.CO astro-ph.GA

Lurdes Ondaro-Mallea , Raul E. Angulo , Boryana Hadzhiyska , Joop Schaye This is my paper · ORCID
classification astro-ph.COastro-ph.GA
keywords kineticSunyaev-Zel'dovicheffectvelocityreconstructionredshift-spacedistortionsFingers-of-Godbaryonicfeedbackstackedsignalopticaldepthnon-linearvelocities
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 shows that the stacked kinetic Sunyaev-Zel'dovich (kSZ) signal—a velocity-weighted measurement of the gas around galaxies—is not simply proportional to the mean gas density. The authors decompose the signal into a dominant bulk-flow term and two non-linear corrections, and show that whether these corrections appear depends entirely on how the stacking velocity is estimated. When velocities are reconstructed from linear theory in real space (an idealized, unobservable case), the non-linear terms cancel and the signal traces the mean optical depth to within a few percent. But with realistic redshift-space distortions, reconstruction errors correlate with the halo environment and the direction of motion, producing a net suppression of about 10 percent on small scales, driven by Fingers-of-God motions of satellite galaxies. These corrections are gravitational in origin and only weakly sensitive to baryonic feedback, and they already reach the 1–2 sigma level for current CMB-galaxy stacks.

What carries the argument

The key object is the exact decomposition of the velocity-weighted stacked kSZ estimator into three contributions: the mean bulk-flow term (proportional to the mean optical depth times the rms halo velocity), the density–bulk-flow correlation term, and the velocity-decorrelation term. The central identity is the linearized continuity equation used to reconstruct velocities from the smoothed galaxy density field, with the density field built either in real space or redshift space. The argument turns on how these terms couple to the stacking velocity: linear real-space reconstruction filters out the small-scale density–velocity correlations that source the non-linear terms, while redshift-spac

What would settle it

A direct simulation test would compare the stacked kSZ signal computed when gas bound to satellite subhaloes keeps its own velocity instead of being forced to the host-halo velocity; a change larger than ~10 percent on small scales would falsify the correction mechanism. Alternatively, a future survey achieving sub-3-percent statistical errors on the small-scale profile could check for the predicted ~10 percent suppression (or ~5 percent with large smoothing); its absence would rule out the model.

Watch

Extended reading notes

Core claim

The central discovery is the identification of the two non-linear velocity terms in the stacked kSZ estimator—the density–bulk-flow correlation and the velocity-decorrelation term—and the demonstration that both are dominated by non-linear gravitational dynamics rather than by baryonic physics. When stacking with true halo velocities, each of these terms individually reaches up to half the total signal but largely cancels, leaving a residual 10–20 percent contribution. When velocities are reconstructed linearly in real space, the reconstructed velocity carries no small-scale non-linear information, so both terms vanish and the signal traces the mean optical depth within a few percent. When r

Load-bearing premise

The result rests on the assumption that ionized gas around satellite galaxies is largely stripped and therefore moves with the host halo rather than with the satellite's orbital velocity; if satellites retain significant bound gas that moves with them, the predicted small-scale suppression changes.

Editorial extensions

If this is right

  • Current measurements are consistent with the mean bulk-flow approximation at the 1–2 sigma level; next-generation CMB surveys will make the non-linear suppression statistically significant, so models must account for it.
  • The mean optical depth can be recovered unbiasedly either by smoothing the reconstruction to large scales (which reduces the suppression to about 5 percent) or by jointly modelling the two non-linear terms with simulations.
  • Because the non-linear terms are gravitational in origin, they can be calibrated with gravity-only simulations including baryon-painted densities; the baryonic contribution through gas velocities alone is below 1 percent.
  • The two non-linear terms must be modelled together; modelling only one introduces errors of roughly 50 percent, while neglecting both introduces errors of only 10–20 percent.
  • There is a direct trade-off between signal-to-noise and modelling simplicity: aggressive reconstructions boost S/N but require simulation-based modelling, while conservative reconstructions simplify interpretation.

Reading between the lines

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

  • If the satellite gas-stripping assumption is wrong—if satellites retain enough bound gas to share their orbital motion—the small-scale suppression would be larger and depend more strongly on the satellite population; this could be tested directly in simulations that resolve gas around infalling satellites.
  • A practical strategy for upcoming surveys might be to run two reconstructions, one aggressive for maximizing signal and one conservative for estimation, and to treat the difference as a systematic error budget.
  • The near-cancellation of the two non-linear terms suggests that analytic models of the stacked kSZ effect that capture only one term may be less accurate than models that ignore both; future effective models should either omit both or include both consistently.
  • The insensitivity to baryonic feedback implies that any measured disagreement between stacked kSZ and X-ray-based gas fractions cannot be attributed to the non-linear velocity correction, strengthening the case that the discrepancy reflects real baryonic physics.
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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

2 major / 4 minor

Summary. This paper studies the velocity-weighted stacked kinetic Sunyaev-Zel'dovich (kSZ) signal using the FLAMINGO hydrodynamical simulations and DESI-like mock galaxy samples (LRG, BGS, ELG). The authors derive an exact decomposition of the estimator into a mean bulk-flow term, a density-bulk flow correlation term, and a velocity-decorrelation term. They then evaluate each term for three stacking-velocity choices: true halo velocities, linearly reconstructed velocities in real space, and linearly reconstructed velocities in redshift space. They find that the two non-linear terms individually can be large but cancel substantially; with real-space linear reconstruction the non-linear terms become negligible, while including redshift-space distortions produces a scale-dependent ~10% suppression on small scales that they attribute primarily to satellite Fingers-of-God. They further show that the non-linear terms are insensitive to baryonic feedback at the 5-10% level, with gas-velocity effects below 1%, and they discuss the implications for current and future kSZ analyses, including a trade-off between smoothing scale and signal-to-noise.

Significance. If the results hold, this is a valuable and timely contribution to the interpretation of stacked kSZ measurements. The algebraic decomposition in Eq. (7) is exact and clarifies which physical effects can enter the estimator, and the use of realistic FLAMINGO mocks with multiple feedback variants gives the main conclusions a solid basis. The paper is careful to compute all non-linear terms directly from simulation fields rather than fitting them to the target observable: there are no free parameters tuned to the kSZ signal. The main strength is the clear demonstration that the modelling strategy must depend on how the stacking velocity is constructed, and that real-space linear reconstruction provides a useful theoretical benchmark. The sensitivity of the non-linear terms to baryonic feedback is quantified explicitly. However, the paper's headline result, the ~10% RSD-driven small-scale suppression attributed to satellite Fingers-of-God, rests on a satellite-gas assumption that is not directly verified in the same simulations, and the ELG sample is acknowledged to be under-resolved. These issues need to be addressed before the central quantitative claim can be fully accepted.

major comments (2)
  1. [Section 3.3.1 / Eq. (4) / Section 4.3.2] The headline small-scale suppression in the RSD case is attributed to satellite Fingers-of-God, and the decomposition that leads to this attribution uses v0 = v_h for satellite galaxies in Eq. (4). The justification is that ionized gas around satellites is largely stripped and therefore moves with the host halo, but this is supported only by citations to He et al. (2026) and Contreras et al. (2026) and is not checked in FLAMINGO, the same simulation used to produce the stacks. If a non-negligible fraction of gas retains the satellite's orbital velocity, v' in Eq. (4) contains a coherent satellite-velocity component, changing the velocity-decorrelation term Cov(p', v_stack) in Eq. (7) and thereby both the amplitude of the ~10% suppression and its satellite attribution. Appendix A tests the alternative subhalo-velocity choice only for the true-velocity stack, where it changes the profile b
  2. [Section 3.2 / Section 3.3.2 / Section 5] The ELG-like sample is explicitly acknowledged to be under-resolved in FLAMINGO: the adopted mean halo mass is 10^12.4 h^-1 M_sun rather than the target 10^12.2 h^-1 M_sun, and the reconstructed-velocity cross-correlation is r ~ 0.74, differing from the r ~ 0.55 obtained with Abacus HOD catalogs. Despite these caveats, Figure 6 and the reported 0.31-sigma consistency for ELGs are presented as part of the main cross-sample results. The statement that the ELG signal is consistent with the mean bulk-flow model is therefore not robust. The authors should either calibrate the ELG mock against a higher-resolution simulation or an updated HOD model, or explicitly downgrade the ELG-specific quantitative conclusions to indicative rather than quantitative.
minor comments (4)
  1. [Sections 4.1-4.4 / Figures 1, 4, 5] No error bars or finite-volume uncertainties are shown for the simulated stacked profiles. Given that the paper makes percent-level quantitative claims, a statement about the statistical precision of the mock stacks (e.g., from bootstrap or realization scatter) would be helpful.
  2. [Section 5.1.1] The sentence 'One might expect RSD to simply reduce the overall amplitude of the stacked kSZ signal through the lower r' is confusing because Eq. (2) is explicitly normalized by r, and the mean bulk-flow term in Eq. (7) is independent of r. Consider rephrasing to clarify that the concern is about the raw stacked amplitude before normalization.
  3. [Section 3.3.1] The statement that using the centre-of-mass velocity of gas particles produces no appreciable difference should specify that this verification applies to host haloes. For satellites, the corresponding check is not provided, which is directly related to the major comment above.
  4. [Section 3.2] The ELG sample caveat should be stated more prominently, ideally in the abstract or the introduction of the cross-sample results, since the current text in Section 3.2 somewhat understates the impact on the ELG-related conclusions.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: non-linear kSZ terms are direct simulation measurements; satellite-stripping prior is an input, not a fitted prediction.

full rationale

The paper's derivation chain is an exact decomposition of the stacked kSZ estimator (Eqs. 2-7) into a mean bulk-flow term and two non-linear terms. These terms are computed directly from FLAMINGO simulation fields and reconstructed velocities; no parameter is fitted to the target kSZ signal, and the DESI/ACT covariance enters only to quantify the statistical significance of the deviations, not to shape them. The main claims that real-space linear reconstruction suppresses non-linear terms to <~2% and that RSD reintroduce a ~10% small-scale suppression, primarily through satellite FoG distortions, are simulation measurements (Figs. 1, 4, 7), not consequences of the definitions. The only externally loaded physical prior is the satellite velocity assignment in Sec. 3.3.1: 'For satellite galaxies, we use the velocity of their host halo rather than that of the subhalo or satellite itself... However, the ionized gas surrounding satellites is largely stripped and therefore does not follow this orbital motion (He et al. 2026; Contreras et al. 2026).' This is a physical assumption rather than a circular reduction: the total simulated kSZ profile is computed from the gas momentum field, so the prior affects only the term-by-term decomposition and the interpretation, not the total signal. Even if this prior were wrong, the paper's quantitative RSD result would remain a definite simulation output; the stripping assumption is therefore a robustness/correctness concern, not a self-consistent derivation loop. Self-citations are used for standard reconstruction methods and previous measurements, but the central results are derived in this paper from published simulations and do not reduce to those citations. Accordingly, no prediction is equivalent to its input by construction; score 1 reflects one non-load-bearing self-citation-supported physical assumption.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

No free parameters are fitted to the target observables. Analysis choices (smoothing lengths, mesh size, projection thickness, beam width) are varied but do not constitute fitted parameters. The only external inputs are the DESI DR2×ACT covariance matrices used for significance and the lensing-mass constraints used for sample selection.

assumptions (6)
  • domain assumption The linearised continuity equation (Eq. 9) with constant linear bias b recovers the large-scale velocity field sufficiently accurately.
    Used to reconstruct stacking velocities in real and redshift space; reconstruction errors beyond r≈0.7 are the source of the RSD suppression.
  • domain assumption The ionized gas around satellite galaxies is stripped and follows the host halo velocity rather than satellite orbital motion.
    Central to the definition of v0 for satellite galaxies and to the size of the velocity-decorrelation term and FoG-driven suppression.
  • domain assumption FLAMINGO simulations faithfully reproduce the gas density and velocity fields around the three galaxy samples at scales 0.5–10 h⁻¹Mpc.
    All quantitative results are measured from these simulations; ELG resolution is acknowledged as limited.
  • domain assumption Projecting gas within a 20 h⁻¹Mpc shell is equivalent to full line-of-sight projection for the stacked signal.
    Stated as checked in Section 3.4, but the convergence itself is not shown.
  • standard math In linear theory, density and velocity are uncorrelated on scales r<50 h⁻¹Mpc so Cov(τ,v0 vstack)=0 and v'=0.
    Justifies calling the two covariance terms 'non-linear'; this is the baseline against which the simulation results are measured.
  • standard math The mean optical depth is proportional to the projected gas mass with a fixed constant at low redshift.
    Section 2 footnote: used to interchange τ and projected gas mass.

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Pith. "Pith review of Interpreting the stacked kinetic SZ effect I: velocity reconstruction and non-linear velocity effects." pith.science (2026). https://pith.science/paper/XVJOOTIH

@misc{pith2026260723339,
  author       = {Pith},
  title        = {Pith review of: Interpreting the stacked kinetic SZ effect I: velocity reconstruction and non-linear velocity effects},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XVJOOTIH}},
  note         = {Machine review of arXiv:2607.23339}
}
abstract

The stacked kinetic Sunyaev-Zel'dovich (kSZ) signal probes the velocity-weighted projected gas momentum around galaxies, and is emerging as a powerful probe of gas fractions and baryonic feedback. Its interpretation, however, rests on several assumptions that we test in this pair of companion papers. Using the FLAMINGO hydrodynamical simulations and DESI-like galaxy mocks for luminous red galaxies (LRGs), the bright galaxy sample (BGS), and emission-line galaxies (ELGs), we identify the ingredients required to model the signal to better than $10\%$. This first paper focuses on velocities. We decompose the signal into a dominant bulk-flow term, proportional to the mean optical depth, plus non-linear terms arising from the small-scale gas momentum and its coupling to the stacking velocity. When the stacking velocities are reconstructed from linear information in real space alone -- an idealisation which is not possible in practice -- the non-linear terms cancel and the signal traces the mean optical depth to within a few per cent. When the stacking velocity instead retains non-linear information or is affected by redshift-space distortions, the non-linear terms suppress the signal by $10-20\%$: a $1-2\sigma$ effect for current data that is expected to be statistically significant for upcoming surveys, and one that depends only weakly on baryonic feedback. Our results reveal a trade-off: velocity estimators that retain small-scale information boost signal-to-noise but require simulation-based modelling, whereas conservative reconstructions simplify the interpretation at the cost of signal-to-noise.

Figures

Figures reproduced from arXiv: 2607.23339 by the authors.

Figure 1
Figure 1. Decomposition of the velocity-weighted stacked kSZ signal for the full DESI-like LRG galaxy sample. Columns show results for different stacking velocities: the true halo velocity (left), the reconstructed velocity in real space (middle), and the reconstructed velocity in redshift space including RSD (right). Upper panels show profiles as a function of projected radius, while lower panels show each component normaliz… view at source ↗
Figure 2
Figure 2. Schematic diagram illustrating the physical origin of the non-linear velocity terms in the velocity-weighted stacked kSZ signal. In the presence of massive structures in the environment of a halo, its gravitational potential attracts material towards it. In projection, this process creates a positive correlation between projected density and halo velocities, as well as local decorrelation of velocities along the lin… view at source ↗
Figure 3
Figure 3. Correlation coefficient 𝑟 between the stacking velocity and the gas density (top row) or gas velocity (bottom row) around halos of DESI-like LRGs. Halos are located at the origin of each panel and move in the positive line-of-sight direction (arrows), where massive structures lie on average. Red indicates positive correlation, blue negative, and white no correlation. The top row shows the correlation with the enviro… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Velocity-weighted stacked kSZ signal around central (upper row) and satellite (lower row) galaxies in the DESI-like LRGs, normalized by the mean bulk flow contribution of the gas – 𝑇ksz/⟨𝜏⟩𝑣 ℎ rms. Columns show results for stacking with true halo velocity (left), the r…
Figure 5
Figure 5. Figure 5: Percentage impact of baryonic physics on the non-linear contribution to the stacked kSZ signal (𝑇 nl = 𝑇ksz − ⟨𝜏⟩𝑣 ℎ rms) of DESI-like LRGs, relative to the mean bulk flow contribution without baryonic effects – (𝑇 nl gas − 𝑇 nl dm)/⟨𝜏dm⟩𝑣 ℎ rms. The dm underscript den…
Figure 6
Figure 6. Figure 6: Stacked kSZ profiles obtained using different stacking-velocity estimators for DESI-like LRG (left), BGS (middle), and ELG (right) samples. Upper panels show the predicted signal using the true halo velocity (blue), reconstructed velocity in real space (orange), and re…
Figure 7
Figure 7. Figure 7: Suppression of the measured kSZ signal relative to the mean bulk flow at 𝜃 = 1 arcmin using a linear velocity reconstruction in redshift space (upper panel), and the cross-correlation coefficient between the true and reconstructed velocities, 𝑟 (lower panel), as a func…

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Reviewed July 31, 2026 · model on record in the stance chip above.