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First Constraints from Marked Angular Power Spectra with Subaru Hyper Suprime-Cam Survey First-Year Data

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Marked angular power spectra, applied here to real lensing data for the first time, tighten S8 by about 43 percent over the standard spectrum, giving S8 = 0.807 ± 0.024.

desk verdict First marked-spectra weak lensing analysis: method is real, but the headline S8 is not yet calibrated. read the letter →

arxiv 2507.12315 v1 pith:DKLGK4BF submitted 2025-07-16 astro-ph.CO

Jessica A. Cowell , Joaquin Armijo , Leander Thiele , Gabriela A. Marques , Camila P. Novaes , Daniela Grandón , Sihao Cheng , Masato Shirasaki
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David Alonso Jia Liu
This is my paper
classification astro-ph.CO
keywords markedangularpowerspectraweaklensingconvergenceS8clusteringamplitudenon-GaussianinformationHyperSuprime-CamYear1Gaussianprocessemulatorhigher-orderstatisticscosmologicalparameterconstraints
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 is the first to apply marked angular power spectra to real weak-lensing data. The idea is simple: before measuring angular power spectra of the convergence field $\kappa$, weight the field by a non-linear mark function of its smoothed version, $\Delta(\kappa)=m(\kappa_\theta)\,\kappa$, so that different density environments contribute with different weights and higher-order information enters an otherwise standard two-point statistic. Using HSC-Y1 convergence maps, the authors combine three complementary mark functions and report that the joint marked auto- and cross-spectra tighten the clustering parameter $S_8\equiv\sigma_8\sqrt{\Omega_{\rm m}/0.3}$ by about 43 percent compared with the standard power spectrum alone, giving $S_8=0.807\pm0.024$. If correct, this makes marked spectra a computationally cheap way for current and future surveys to recover non-Gaussian information that two-point analyses miss.

What carries the argument

The central object is the marked convergence field $\Delta(\kappa)=m(\kappa_\theta)\,\kappa$, where $m$ is a mark function and $\kappa_\theta$ is the convergence field smoothed by a Gaussian of width $\theta\in\{2',4',10'\}$; its angular power spectrum is computed with the same mask-corrected pseudo-$C_\ell$ machinery as the ordinary spectrum. Three mark functions probe different density environments: a Gaussian-process-shaped weight (A), the rescaled smoothed field (B), and a modified power law that up-weights underdensities (C). The cosmological prediction is carried by a Gaussian-process emulator trained on 100 cosmology-varied N-body simulations spanning $\Omega_{\rm m}$ and $\sigma_8$, with each bandpower emulated separately, while the covariance is estimated from 2268 realisations of a fiducial-cosmology simulation suite and inverted with the Anderson--Hartlap correction. The emulator is what turns the measured spectra into a posterior on $S_8$ and $\Omega_{\rm m}$, so the paper's quoted improvements stand or fall on its fidelity.

What would settle it

Build the emulator from a single, higher-resolution simulation suite (or one including baryonic feedback), re-infer $S_8$ from the same HSC-Y1 data vector, and watch the $\ell_{\rm max}$ dependence: the Appendix D rise of $S_8$ with scale predicts that training on simulations with more small-scale power should flatten that trend and pull the fiducial value below $0.807$, while removing mark B, the largest source of simulation-suite residuals in Appendix B, should barely move the constraint if the multi-mark result holds.

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Extended reading notes

Core claim

The paper's central claim is that marked angular power spectra are a practical higher-order statistic for weak lensing, not just a theoretical construct. Starting from HSC-Y1 convergence maps, the authors build nine marked fields from three mark functions (a Gaussian-process-shaped weight, the rescaled smoothed field $\kappa_\theta/\sigma(\kappa_\theta)$, and a modified power law that up-weights underdense regions) at smoothing scales of 2, 4, and 10 arcminutes, and measure their auto-spectra and cross-spectra with the original $\kappa$ field. Combining all three marks with the standard spectrum tightens $S_8$ to $0.807\pm0.024$, a factor of 1.43 (32 percent smaller error bars) over the power spectrum alone under identical scale cuts, with the gain driven by the marks having different degeneracy directions in the $S_8$--$\Omega_{\rm m}$ plane. The paper further argues that part of the improvement is scale mixing: the non-linear mark lets small-scale Gaussian power leak into large-scale multipoles, so the marked spectra are a practical proxy for bispectrum- and trispectrum-like information rather than a pure measurement of non-Gaussianity, while the $m_B$ cross-spectrum is a projected bispectrum integral and the auto-spectrum splits into Gaussian and connected-trispectrum parts. Systematic tests on baryonic feedback, intrinsic alignments, photometric-redshift choice, and multiplicative shear bias keep $S_8$ shifts within about $0.4\sigma$ at the adopted scale cuts.

Load-bearing premise

The result stands or falls on whether a Gaussian-process emulator trained on 100 gravity-only N-body simulations predicts the marked angular power spectra of the real universe on the scales used in the analysis, and the paper itself documents the risk: a systematic offset between its two simulation suites and a rise in the inferred $S_8$ with smaller scales in real data that the simulations do not reproduce.

Editorial extensions

If this is right

  • No single mark matches the trio: marks B and C have nearly orthogonal degeneracy directions in the $S_8$--$\Omega_{\rm m}$ plane, which the paper identifies as the source of the 1.43$\times$ gain from combining them.
  • Part of the constraining power of marked spectra comes from Gaussian small-scale information leaking into large-scale multipoles through the non-linear mark, so the method is a practical proxy for higher-order correlations rather than a pure non-Gaussian statistic.
  • With smoothing scales and scale cuts chosen so that each tested systematic shifts $S_8$ by less than roughly $0.4\sigma$, the baseline analysis keeps $\ell_{\rm max}=1500$ and the inferred $S_8$ stays within that tolerance for baryons, intrinsic alignments, photo-$z$ choice, and multiplicative shear bias.
  • Mark B dominates the $\Omega_{\rm m}$ constraining power, with an error about a third of the prior width, although the paper cautions that its $\Omega_{\rm m}$ value is affected by emulator accuracy.
  • Leaving out cross-correlations between tomographic redshift bins leaves information unused; the paper notes these could tighten constraints further.

Reading between the lines

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

  • If the 43 percent gain survives in Stage-IV surveys with much lower shape noise, marked spectra become one of the cheapest non-Gaussian additions to a lensing pipeline, since they reuse the standard power-spectrum code path and simulation-based emulators.
  • The scale-mixing decomposition suggests a design principle for future work: comparing marked-spectrum gains across smoothing scales separates Gaussian leakage from genuine non-Gaussian information, and could be used to engineer marks that maximize the truly non-Gaussian component.
  • The rising $S_8$ with $\ell_{\rm max}$ in the real data, absent in simulations, reads as a small-scale modelling deficit; if higher-resolution training shifts the fiducial value, the reported $0.807$ should be revised downward.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper presents the first application of marked angular power spectra to weak lensing data, using HSC-Y1 convergence maps. Marked fields are constructed by weighting the convergence field with three nonlinear mark functions (a Gaussian-process-derived mark, a smoothed-field mark, and a modified White 2016 mark), and their auto- and cross-spectra are combined with the standard convergence power spectrum. A Gaussian-process emulator trained on 100 cosmology-varied N-body simulations is used to model the summary statistics, and a covariance from 2268 pseudo-independent realizations is used for likelihood inference. The baseline analysis yields S8 = 0.807 ± 0.024 and claims a ~43% improvement in the S8 error bar over the standard power spectrum. The paper also tests sensitivity to baryonic effects, intrinsic alignment, photo-z errors, and multiplicative shear bias, and shows that the marked spectra contain bispectrum- and trispectrum-like contributions.

Significance. The paper is a proof-of-concept that marked angular power spectra can be applied to real weak-lensing data and combined with standard spectra to tighten cosmological constraints. If the result holds, it would be a useful addition to the toolkit of higher-order statistics for Stage-IV surveys. The simulation pipeline is detailed, the systematic tests are extensive, and the paper is unusually transparent about its own internal inconsistencies: the simulation-suite offset in Appendix B, the scale-mixing interpretation in Section 4.3, and the unexplained scale-dependent S8 trend in Appendix D. These are genuine strengths. However, the same passages show that the headline improvement factor and the quoted S8 value rest on an emulator that fails an external validation test and on a comparison that is not matched in information content. The central claim is therefore not yet established, although the underlying idea is promising.

major comments (4)
  1. [Section 3.5 and Appendix B] The emulator is validated only by leave-one-out tests inside the cosmo-varied suite. Appendix B provides the crucial external check: feeding the covariance-suite mean data vector through the pipeline systematically overestimates S8 for every ℓmax tested, with the largest spectral residuals in the mark-B cross-spectrum (Fig. B2). Because the same emulator is used for the HSC-Y1 analysis, the reported S8 = 0.807 ± 0.024 inherits this bias. The paper acknowledges the offset but does not correct for it or marginalize over it. The central claim requires either recalibrating the emulator against an independent suite or quantifying the bias in units of the final uncertainty and adding it to the systematic budget.
  2. [Section 4.3, Eq. (14), and the abstract] The decomposition in Eq. (14) shows that the Gaussian (disconnected) part of C^ΔΔ_ℓ is sensitive to the power spectrum at multipoles ℓ ≲ 3200 for θ = 2', far beyond the ℓmax = 1500 applied to C^κκ_ℓ in the baseline comparison. The paper itself concludes that the apparent additional constraining power likely comes from Gaussian fluctuations on smaller scales, not from intrinsic non-Gaussianity. A direct comparison at matched effective information content is therefore not made, and the abstract's statement that marked spectra 'improve constraints on S8 by ≈43% compared to standard two-point power spectra' overstates the improvement as a purely non-Gaussian gain. The claim should be reworded to separate scale mixing from genuine higher-order information, or the power-spectrum baseline should be extended to the same effective scale.
  3. [Appendix D and Figure D1] The HSC-Y1 data show a consistent rise in S8 as ℓmax increases, for both marked and standard spectra, while neither simulation suite reproduces this trend. The baseline scale cut ℓmax = 1500 is chosen in a regime where this trend is already visible. Given the emulator bias demonstrated in Appendix B, the data-versus-simulation mismatch weakens the interpretation of the reported S8 as a cosmology measurement. The paper asserts the bias is within statistical uncertainties, but no quantitative comparison between the observed trend and the simulation-derived uncertainty is provided. The authors should demonstrate explicitly that the scale-dependence seen in Figure D1 is consistent with the covariance-suite validation once the Appendix B offset is accounted for.
  4. [Section 4.1, Section 5, and the abstract] The fiducial S8 value is quoted inconsistently: the abstract and Section 4.1 give S8 = 0.807 ± 0.024, while Section 5 gives S8 = 0.804 ± 0.023. Similarly, the abstract claims an improvement of ≈43%, Section 4.1 states '1.4× smaller error', and Section 5 quotes an improvement factor of ~1.43. These numbers refer to the same baseline analysis but are not mutually consistent in their presentation. The headline number and the claimed improvement factor should be stated once, consistently, with the associated error bars, and the abstract must match the body.
minor comments (6)
  1. [Section 3.6] The stated priors are 'uniform priors on Ωm of [0.1, 0.4] and S8 of [0.5, 0.1]'; the S8 interval is clearly a typo (it should presumably be [0.5, 1.0] or similar, based on Fig. 3), and should be corrected.
  2. [Figure 4 caption] The caption says 'The coloured regions show 1/3σ confidence interval of the underlying cosmology'; this is ambiguous and likely should read '1σ and 3σ confidence intervals'.
  3. [Figure 8] The text above each bar is described as the 'improvement in the value of σ(S8) found from C^κκ_ℓ', but the y-axis is labelled σ(S8) and the bars appear to show absolute errors; the relationship between the labels and the bars should be clarified.
  4. [Appendix B (last paragraph)] In the sentence 'they are almost affected by finite thickness effects', 'almost' appears to be a typo, likely 'also'; this should be corrected for clarity.
  5. [Section 4.3] In Eq. (14) and the surrounding text, the normalization of the marked field Δ(x) is dropped for simplicity, as noted in the footnote; it would be helpful to state explicitly in the main text that the 1/σ(κ_θ) factor is omitted throughout the n-point function expansion.
  6. [Appendix C] The heatmaps in Figure C1 are informative, but the text states that 'white text flags deviations greater than 0.3σ' without explaining the colour scale for values below that threshold; adding a colour bar with the deviation units would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the marked-spectra derivation and S8 likelihood are self-contained forward-modeling exercises, with no fitted parameter renamed as a prediction.

full rationale

The paper's central inference (S8=0.807±0.024) is obtained by comparing HSC-Y1 marked angular power spectra to a Gaussian-process emulator trained on 100 cosmology-varied N-body simulations (Sec. 3.5), using a Gaussian likelihood and MOPED compression (Sec. 3.6). The mark functions are fixed from prior literature (Sec. 2.2) and are not fitted to HSC-Y1 data or to the target S8; the GP-node recalibration is a shape-preserving rescaling of node positions, not a fit of cosmological parameters. The claimed relation to higher-order statistics is derived directly from the definitions: Eq. (13) expresses C^{kappa Delta} as an integral of the projected bispectrum, and Eq. (14) splits C^{Delta Delta} into a disconnected Gaussian piece plus a connected trispectrum; neither equation uses the measured S8 as input. The paper's own caveats in Appendices B and D (a systematic offset when the covariance-suite data vector is passed through the emulator, and a rising S8 with ell_max in real data) are accuracy and validation concerns about the emulator and simulation suite, not circular reductions: the emulator was not calibrated to the HSC measurement, and the offset is reported as a known limitation rather than used to define the result. The 43% improvement claim is a ratio of posterior widths from the same likelihood; although Sec. 4.3 shows part of the gain comes from Gaussian small-scale information leaked through the mark convolution, that is an honest decomposition of the statistic, not a circular re-labelling of the input. Self-citations to Cowell et al. (2024) and companion HSC-Y1 papers supply mark shapes and simulation suites, but they are not used as a uniqueness theorem and the main result is not forced by them. No equation or parameter in the derivation reduces by construction to the target S8 value.

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

No new physical entities are introduced; the marked fields are constructed from the observed convergence field. The free parameters are mark-function hyperparameters, smoothing scales, and the scale-cut choice, all fixed a priori or by robustness tests rather than fitted to the S8 value.

free parameters (6)
  • GP mark kernel amplitude = 20
    Chosen somewhat arbitrarily for mark A (Sec 2.2); authors state it is arbitrary so long as the length scale exceeds node spacing.
  • GP mark kernel length scale = 0.7
    Chosen for mark A (Sec 2.2); authors state the choice is arbitrary.
  • GP mark node positions = rescaled to min/max of each smoothed kappa field
    Nodes are recalibrated per field, redshift bin, and smoothing scale, effectively adjusting the mark shape to each map (Sec 2.2).
  • Mark C parameters p, delta, b = p=0.5, delta=0.02, b=0.1
    Fixed following Massara et al. (2023) and Armijo et al. (2024a) (Sec 2.2).
  • Smoothing scales theta = [2,4,10] arcmin
    Chosen by hand as the mark smoothing scales for the baseline analysis (Sec 3.4).
  • Maximum multipole lmax = 1500
    Selected so that systematic-induced shifts in S8 are <=0.4 sigma (Sec 3.7); other choices give larger shifts (Appendix C).
assumptions (6)
  • domain assumption The N-body simulation suites accurately reproduce HSC-Y1 observations including non-linear structure growth, mask, noise, and galaxy properties.
    The emulator and covariance rely on simulations (Sec 3.2); Appendix B shows a known offset between the two simulation suites, so this is not fully validated.
  • domain assumption The Gaussian process emulator interpolates marked power spectra across Omega_m and S8 with accuracy sufficient for the reported error bars.
    Leave-one-out tests show ~10% scatter and a 2-sigma biased cosmology near the fiducial (Sec 3.5).
  • standard math The Gaussian likelihood with MOPED-compressed data vector is an adequate description.
    Assumed in Sec 3.6.
  • domain assumption The NLA model correctly captures intrinsic alignments for the tested amplitudes.
    Used for IA systematics in Sec 3.7.2.
  • domain assumption MLZ photo-z estimates are unbiased or biases are within the tested alternatives.
    Baseline uses MLZ; FRANKEN-Z and Mizuki shifts are checked but not modeled in the fiducial analysis (Sec 3.7.3).
  • domain assumption The Kaiser-Squires inversion with inpainting recovers the true convergence field on the scales used.
    Sec 3.1 describes map construction; no validation of the inversion is shown.

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Cite this review

Pith. "Pith review of First Constraints from Marked Angular Power Spectra with Subaru Hyper Suprime-Cam Survey First-Year Data." pith.science (2026). https://pith.science/paper/DKLGK4BF

@misc{pith2026250712315,
  author       = {Pith},
  title        = {Pith review of: First Constraints from Marked Angular Power Spectra with Subaru Hyper Suprime-Cam Survey First-Year Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DKLGK4BF}},
  note         = {Machine review of arXiv:2507.12315}
}
abstract

We present the first application of marked angular power spectra to weak lensing data, using maps from the Subaru Hyper Suprime-Cam Year 1 (HSC-Y1) survey. Marked convergence fields, constructed by weighting the convergence field with non-linear functions of its smoothed version, are designed to encode higher-order information while remaining computationally tractable. Using simulations tailored to the HSC-Y1 data, we test three mark functions that up- or down-weight different density environments. Our results show that combining multiple types of marked auto- and cross-spectra improves constraints on the clustering amplitude parameter $S_8\equiv\sigma_8\sqrt{\Omega_{\rm m}/0.3}$ by $\approx$43\% compared to standard two-point power spectra. When applied to the HSC-Y1 data, this translates into a constraint on $S_8 = 0.807\pm 0.024$. We assess the sensitivity of the marked power spectra to systematics, including baryonic effects, intrinsic alignment, photometric redshifts, and multiplicative shear bias. These results demonstrate the promise of marked statistics as a practical and powerful tool for extracting non-Gaussian information from weak lensing surveys.

Figures

Figures reproduced from arXiv: 2507.12315 by the authors.

Figure 1
Figure 1. We illustrate the process of creating marked fields Δ𝑖 , using the example of the convergence field from the HSC-Y1 “wide12h” field with a 10′ smoothing scale in the third redshift bin (0.9 < 𝑧 < 1.2). Left column (top to bottom): example mark functions as a function of the smoothed field 𝑚𝑖 (𝜅𝜃 ); the original convergence field 𝜅, smoothed at 1 ′ ; and the smoothed field 𝜅𝜃 for 𝜃 = 10′ . Middle column: mark functio… view at source ↗
Figure 2
Figure 2. Example correlation matrices for sections of the full covariance matrix. In the first three columns, we show the blocks corresponding to the auto spectra (𝐶ΔΔ ℓ of the three marks, A, B, C, defined in Section 2.2 for smoothing scales of 2 ′ , 4 ′ and 10′ . On the far right, we show the correlation between these marks for the example of 10’. All blocks are before scale cuts. All are shown using the third redshift bin… view at source ↗
Figure 3
Figure 3. Accuracy validation using the leave-one-out method. For each of the 100 cosmologies (shown as points), we remove that simulation from the emulator and use it as an input data vector to evaluate the shift in the inferred values of 𝑆8 (left) and Ωm (right) relative to the true values. Offsets are expressed in units of the posterior standard deviation. The analysis uses the baseline setup with all three mark functions … view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Analysis of the impact of systematic effects on 𝑆8 (left) and Ωm, (right). For each contaminated data vector we repeat the inference and recover the error bars shown. The coloured regions show 1/3𝜎 confidence interval of the underlying cosmology with no systematics add…
Figure 5
Figure 5. Figure 5: Constraints on 𝑆8 and Ω𝑚 using marked power spectra and HSC-Y1 data, using our baseline analysis choice of combining three mark functions (A, B, C) over three smoothing scales of 2’, 4’, 10’, using scale cuts of ℓ < 1500, and no cross correlations between separate tomo…
Figure 6
Figure 6. Figure 6: 𝑆8 constraints from various surveys and methods. The top group in red corresponds to results from CMB surveys, meanwhile, the blue/purple are all from weak lensing. In purple we show the results of the other non-Gaussian (NG) statistics using HSC-Y1, with our result in…
Figure 7
Figure 7. Figure 7: Constraints on Ωm and 𝑆8 = 𝜎8 √︁ Ωm/0.3 from three different marked power spectra using HSC-Y1 data. Δ denotes the marked field, and 𝜅 the original convergence field. The three marks emphasise different regions: A anti-correlates and up-weights medium over- and underde…
Figure 8
Figure 8. Figure 8: Posterior uncertainties on 𝑆8 for different analysis configurations. Results are shown for individual mark choices (A, B, C; in distinct colours) as well as their combination (blue). Within each configuration, we compare the constraints obtained from the correlation fu…
Figure 9
Figure 9. Figure 9: Posteriors of the different combinations of B marked power spectra, using the mark function 𝑚B = 𝜅𝜃 with the HSC-Y1 data. Δ denotes the marked field, while 𝜅 is the original convergence field. We colour the 68% (inner line) and 95% (outer line) confidence intervals con…

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Weighted Webs: Morphology-Informed Marked Fields

    astro-ph.CO 2026-07 conditional novelty 6.0 of 10

    Morphology-based marks (tidal shear and local fractal dimension) add a modest but complementary ~10% Fisher-information gain over density-only marked power spectra for cosmological parameters.

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    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.