Evidence for Intrinsic Galaxy Alignments in Ellipticity Autocorrelations out to $100 h^{-1}\textrm{Mpc}$ from SDSS Galaxies with DESI Imaging

Teppei Okumura

REVIEW 3 major objections 3 minor 48 references

Evidence for Intrinsic Galaxy Alignments in Ellipticity Autocorrelations out to $100 h^{-1}\textrm{Mpc}$ from SDSS Galaxies with DESI Imaging

T0 review · 3 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper reports the first observational evidence that the autocorrelation of galaxy ellipticities—the intrinsic–intrinsic correlation—follows a clean power law out to 100 Mpc in three SDSS galaxy samples.

desk verdict A plausible first 100 Mpc II autocorrelation measurement with a clever basis choice, but the missing PSF/systematics budget keeps the headline claim from being fully secured. read the letter →

arxiv 2507.09756 v2 pith:IA2NBAX7 submitted 2025-07-13 astro-ph.CO astro-ph.GA

Teppei Okumura This is my paper

classification astro-ph.COastro-ph.GA

keywords intrinsicalignmentsellipticityautocorrelationIIcorrelationassociatedLegendrepolynomialslarge-scalestructureredshiftsurveysellipticalgalaxiesDESIimaging

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 Letter reports the first observational evidence that the autocorrelation of galaxy ellipticities—the intrinsic–intrinsic (II) correlation—does not vanish at large scales but follows a clean power law out to $100\,h^{-1}\mathrm{Mpc}$, a scale comparable to the baryon acoustic oscillation length. The measurement uses LRG, LOWZ, and CMASS galaxy samples from SDSS and BOSS over $0.16\leq z\leq 0.70$, with LOWZ and CMASS shapes improved by crossmatching to DESI imaging. The key step is expanding the II(−) correlation in associated Legendre polynomials, which concentrates the linear-order alignment signal into the single $L=4$ multipole and makes the detection visible in every sample. If correct, this establishes galaxy shape autocorrelations as a measurable cosmological observable, opening a window on signals that only live in shape autocorrelations, such as tensor perturbations from a stochastic gravitational-wave background.

What carries the argument

The load-bearing object is the $L=4$ multipole of the II(−) correlation, $\tilde{\xi}_{-,L}(r)$, obtained by expanding the density-weighted ellipticity autocorrelation in normalized associated Legendre polynomials $\Theta_L^{m=4}(\mu_r)$. Because the line-of-sight projection factor $(1-\mu_k^2)^2$ in the NLA power spectrum appears only in the II(−) statistic, the linear-order signal compresses into a single multipole, unlike the standard Legendre expansion that spreads it over $\ell=0,2,4$. On the model side, the paper uses the nonlinear alignment model with a shape-bias parameter $b_K$ and a finger-of-God damping term, with the nonlinear matter power spectrum supplied by revised Halofit.

What would settle it

Rotate every galaxy ellipticity by 45 degrees to form a B-mode estimator, or replace the galaxy shapes with the shapes of unresolved stars at the same positions, and measure the same $L=4$ correlation out to $100\,h^{-1}\mathrm{Mpc}$; if a comparable power-law signal appears, the claimed detection is dominated by additive systematics rather than intrinsic alignments.

Watch

Extended reading notes

Core claim

The central claim is that the II(−) ellipticity autocorrelation, expanded in the associated Legendre basis, is detected as a smooth power law out to $100\,h^{-1}\mathrm{Mpc}$ in all three samples. Fitting the nonlinear alignment (NLA) model with a Gaussian finger-of-God damping to the $L=4$ multipole $\tilde{\xi}_{-,L}(r)$ gives shape-bias amplitudes $-b_K\sigma_8 = 0.2358$, $0.1198$, and $0.1174$ for LRG, LOWZ, and CMASS, respectively, with quoted errors near $0.01$. The paper also shows that combining II(+) and II(−) improves the detection significance by about 10% even though both are derived from the same $E$-mode power spectrum. These results are presented as the first unambiguous measurement of intrinsic shape autocorrelations at BAO-like scales, achieved by the basis choice and by the deeper DESI imaging.

Load-bearing premise

The measurement is read as intrinsic galaxy alignments, so the ellipticity autocorrelation must be dominated by true galaxy shapes rather than by observational systematics such as image-blurring distortions or weak-lensing shear; the analysis does not report a point-spread-function correction or null-test step to exclude those contaminants.

Editorial extensions

If this is right

Galaxy shape autocorrelations can now be used as a large-scale structure probe at BAO-like scales, not just as a small-scale signal.
Combining the II(+) and II(−) statistics yields about a 10% gain in detection significance, even though both derive from the same $E$-mode power spectrum.
The associated-Legendre basis puts the entire linear-order II(−) signal into a single multipole, so it is the natural expansion for future intrinsic-alignment analyses.
Shape autocorrelations open a new observational window on signals uniquely encoded in them, such as tensor perturbations from a stochastic gravitational-wave background.
The same framework can be extended to wider redshift ranges and larger volumes with newer imaging data.

Reading between the lines

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

If the detection survives a B-mode null test and point-spread-function contamination checks—neither is reported here—the quoted amplitudes are intrinsic; otherwise they are upper limits on the combined intrinsic-alignment and systematic signal.
At 100 Mpc scales, intrinsic alignments are large enough that cosmic-shear surveys will need to model II correlations out to BAO-like scales, not only on small scales.
The associated-Legendre compression may transfer to other projected spin-2 statistics, such as cosmic shear or CMB polarization, where a single multipole could capture the leading signal.
If the NLA model truly fits the full range, the scale dependence of $b_K$ can now be measured out to 100 Mpc, testing tidal-alignment theory in a previously inaccessible regime.

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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

You should know this paper has a genuine new result: it pushes intrinsic ellipticity autocorrelations out to 100 h^-1 Mpc for three independent SDSS/BOSS samples, using an associated-Legendre basis that concentrates the II(-) signal into a single L=4 multipole. That basis choice is well motivated, and it clearly works—the eξ−,L data show a smooth power-law out to 100 Mpc for LRG, LOWZ, and CMASS, with NLA model fits at χ2/dof near unity. The DESI imaging crossmatch for LOWZ and CMASS is a sensible way to get deeper, cleaner shapes, and it visibly improves on the previous 30 Mpc detection in Okumura et al. (2009). That is a real step forward for the II autocorrelation subfield, not just a re-packaging.

The soft spots are mostly about systematics, and they are not minor for a first-detection claim. There is no PSF correction step, no star-galaxy null test, no B-mode test, and no subtraction of cosmic-shear contamination. The LRG shapes are isophotal r-band measurements at 25 mag arcsec^-2, which are fine for bright ellipticals but not PSF-deconvolved; the DESI-matched shapes have no shape-measurement pipeline described. Coherent PSF anisotropy on degree scales could plausibly produce a smooth power-law in the L=4 associated-Legendre mode over this angular range, and the paper gives no evidence that this is absent. I also note that the detection significance is only quoted via NLA fit parameters (bKσ8 divided by its error); there is no model-independent significance like Δχ2 against a null hypothesis, and the jackknife covariance is unvalidated against mocks. The CMASS II(+) fit required a post-hoc scale cut to reach χ2/dof~1—a small red flag but not fatal to the main II(-) result.

That said, the central claim is not circular: the correlations are measured directly, the NLA model is fitted, and the three independent samples agree in amplitude trend, so the evidence for real II signal at large scales is fairly robust. The missing systematics budget is a load-bearing caveat, not a refutation. If PSF or lensing contamination is at the level the authors implicitly assume, the result stands; if not, the amplitudes could be biased.

For a referee, I would send this to peer review—it deserves serious scrutiny because the result, if correct, opens shape autocorrelations as a probe on BAO-like scales and for gravitational-wave signatures. The referee should demand: a PSF null test (star shapes on the same estimator), a B-mode check, and an explicit detection significance with a documented covariance. The paper is a Letter, so these can be compact, but they need to be there.

For your own reading: worth a look if you work on intrinsic alignments or large-scale structure, but don't cite the 100 Mpc claim until the systematics tests appear.

Referee Report

3 major / 3 minor

Summary. This paper measures the intrinsic-intrinsic (II) ellipticity autocorrelation function from three SDSS galaxy samples (LRG, LOWZ, CMASS) over 0.16≤z≤0.70, using DESI Legacy Survey imaging for the LOWZ and CMASS shapes. The authors expand the II(−) correlation in the associated Legendre basis and report that the L=4 mode shows a clear power-law trend out to 100 h−1 Mpc for all three samples. They fit a nonlinear alignment (NLA) model with parameters (bKσ8, σv) and obtain reduced χ2 values near unity for the II(−) associated-Legendre fits. They claim this is the first observational evidence for intrinsic alignments in ellipticity autocorrelations at these scales.

Significance. The claimed result, if robust, would be a notable observational advance: it would extend shape autocorrelation measurements to BAO-like scales and open a new probe of signals such as gravitational-wave imprints. The associated-Legendre expansion is well motivated and clearly presented, and the consistency of a power-law signal across three independent samples is encouraging. However, the detection claim is not yet secured because the paper reports no systematics tests (PSF null tests, B-mode tests, or cosmic-shear subtraction) and gives no quantitative detection significance. The strengths are the novel basis choice and the use of deeper imaging for LOWZ and CMASS; the weaknesses are the missing systematics budget and the absence of a model-independent significance statement.

major comments (3)

[Sections 2 and 3, Eqs. (1)-(3)] The estimator in Eq. (3) treats the measured shapes as intrinsic alignments, but no PSF correction, stellar-shape null test, B-mode test, or cosmic-shear subtraction is reported for any of the three samples. Because the linear-order II(−) signal is compressed into a single associated-Legendre mode, a coherent PSF anisotropy correlated on degree scales could produce a spurious power-law signal in eξ−,L. Please add null tests (e.g., cross-correlation of galaxy shapes with stellar shapes, a B-mode measurement, and a test against PSF size or seeing) or explicitly quantify the maximum allowable systematics amplitude.
[Section 4.2, Table 1, and Abstract] No detection significance is stated anywhere in the paper. The abstract claims that joint analysis increases the detection significance by ~10%, but the significance is not defined; the quoted bKσ8 errors are model-dependent and do not by themselves quantify the evidence against the null hypothesis bK=0. Please report for each sample the Δχ2 or signal-to-noise ratio of the eξ−,L measurement against the null, and use that quantity to support the 'first evidence' claim.
[Section 4.2, CMASS II(+) fit] The II(+) standard-Legendre fit for CMASS has reduced χ2=2.909 (Table 1), i.e., a poor fit. The text states that excluding data with rmin=25 h−1 Mpc brings χ2/dof to ~1, but this alternative fit is not shown in Table 1, and the joint analyses (rows 4 and 5 of Table 1) do not specify which scale cuts are used for each statistic. Please make the scale cuts explicit for every entry in Table 1 and report the resulting χ2 and parameter constraints for the rmin=25 case.

minor comments (3)

[Sections 1 and 2] The instrument is referred to as the 'Dark Energy Spectrograph Instrument' twice; the correct name is the Dark Energy Spectroscopic Instrument (DESI).
[Section 4.1 and Figures 1-2] The 'Linear' predictions use the same nonlinear Halofit power spectrum as the 'Nonlinear' model and differ only in the FoG damping; please clarify this in the text or label the curves as 'Linear RSD' and 'Nonlinear RSD' to avoid confusion.
[Section 3] Please provide a brief statement on the jackknife implementation, e.g., the number of jackknife regions and the geometry, so that the covariance estimate is reproducible.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the II measurements are direct data products, and the NLA model is fitted to them rather than used to generate the claimed signal.

full rationale

The core detection is not circular. The ellipticity autocorrelation functions ξ±(r) are measured directly from galaxy shapes via the pair-based estimator in Eq. (3); they do not depend on the NLA model or on any fitted parameter. The NLA model appears only in Sec. 4.1, where it is used to interpret the measured multipoles, and in Sec. 4.2 the free parameters (bKσ8, σv) are fitted to the data (Table 1). Thus the quoted amplitudes are parameter estimates, not predictions derived from the same quantities in a way that would force the conclusion. The associated-Legendre expansion of Eq. (5) is a linear recombination of the measured ξ−(r, μr), and the claim that the linear-order signal is concentrated in L=4 follows from the E-mode power-spectrum expression in Eq. (8) and the Appendix formulas (Eqs. A1–A4), which are given in the paper rather than imported solely from a self-citation. The use of previous work, including Okumura et al. (2024) and Okumura & Taruya (2023), is not load-bearing in a circular sense: the model formulas are reproduced in the Appendix, and the earlier LRG measurement is an independent earlier data product. The statement that the improved detection is 'entirely due to the improved basis choice' is an assessment of the analysis method, not a claim that the data were generated by the model. Concerns about PSF anisotropy or lensing contamination would be systematics issues, not circularity, because the signal is not defined in terms of, or constructed from, the model being tested. No step in the derivation reduces by definition to its own input.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central detection rests on a fitted NLA amplitude, an assumed jackknife covariance estimator, and an assumed clean shape measurement. No new particles, forces, or entities are introduced. The associated Legendre basis is mathematically standard and previously developed, so it is not an invented entity.

free parameters (3)

bK sigma8 (shape bias amplitude times sigma8) = LRG II(-) associated: -bK sigma8 = 0.2358 +/- 0.0170; LOWZ: 0.1198 +/- 0.0102; CMASS: 0.1174 +/- 0.0083
Per-sample amplitude fitted to the II correlations; the nonzero value is the basis for the detection claim (Table 1).
sigma_v (nonlinear velocity dispersion) = Not quoted as a point estimate; contours shown for LOWZ in Figure 3
Free parameter in the Gaussian Finger-of-God damping DFoG; fitted jointly with bK sigma8.
r_min scale cut for CMASS II(+) fit = 25 h^-1 Mpc (default is 6 h^-1 Mpc)
Adopted post hoc to bring the CMASS II(+) reduced chi2 near unity; affects model validation for II(+), not the central II(-) claim.

assumptions (5)

domain assumption NLA model: intrinsic ellipticity is linearly proportional to the nonlinear tidal field (Equation 6, after Catelan et al. 2001; Hirata and Seljak 2004).
Used for all model predictions; higher-order shape bias terms are neglected and later invoked to explain the II(+) small-scale mismatch.
domain assumption Jackknife resampling yields reliable covariance when shot noise dominates.
Stated in Section 3; no validation against mock catalogs or alternative covariance estimators is provided.
domain assumption SDSS and DESI imaging shape measurements accurately represent intrinsic galaxy orientations, with no significant PSF anisotropy, additive bias, or cosmic shear contamination.
The measured autocorrelations are interpreted as intrinsic alignments, but no systematics budget is presented in the paper.
domain assumption Flat LCDM cosmology from Planck 2018 is adopted.
Comoving distances and the Halofit nonlinear matter power spectrum are fixed to this cosmology; a different cosmology would alter the scale mapping and model predictions.
standard math Line-of-sight projection of a spin-2 field leads to an associated Legendre expansion with m=4.
Derived in prior work (Kurita and Takada 2022; Okumura et al. 2024); used here without re-derivation.

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Cite this review

Pith. "Pith review of Evidence for Intrinsic Galaxy Alignments in Ellipticity Autocorrelations out to $100 h^{-1}\textrm{Mpc}$ from SDSS Galaxies with DESI Imaging." pith.science (2026). https://pith.science/paper/IA2NBAX7

@misc{pith2026250709756,
  author       = {Pith},
  title        = {Pith review of: Evidence for Intrinsic Galaxy Alignments in Ellipticity Autocorrelations out to $100 h^-1\textrmMpc$ from SDSS Galaxies with DESI Imaging},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IA2NBAX7}},
  note         = {Machine review of arXiv:2507.09756}
}

abstract

Measuring the autocorrelation of galaxy shapes, known as the intrinsic-intrinsic (II) correlation, is important for both cosmology and understanding the formation of massive elliptical galaxies. However, such measurements are significantly more challenging than those of the cross-correlation with galaxy density (GI correlation) due to the much lower signal-to-noise ratio. In this Letter, we report the first observational evidence for large-scale intrinsic alignments measured from the ellipticity autocorrelations, extending out to $100\,h^{-1}\,{\rm Mpc}$. From the Sloan Digital Sky Survey (SDSS) and SDSS-III Baryon Oscillation Spectroscopic Survey, we analyze, over the redshift range $0.16\leq z\leq 0.70$, luminous red galaxy, LOWZ, and CMASS galaxy samples, the latter two of which are crossmatched with high-quality Dark Energy Spectrograph Instrument imaging data. By expanding one of the two II correlation functions, II($-$), in terms of the associated Legendre polynomials, we effectively isolate the line-of-sight projection effects and enhance the signal. The resulting correlation for all three samples exhibits a clear power-law form. We also show that jointly analyzing the two II correlations, II($+$) and II($-$), increases the detection significance by $\sim 10\%$, even though both are derived from the same $E$-mode power spectrum. Importantly, this measurement opens a new observational window for probing signals uniquely encoded in shape autocorrelations, such as tensor perturbations from the gravitational waves. Our analysis establishes a practical framework for extracting such effects.

Figures

Figures reproduced from arXiv: 2507.09756 by the authors.

**Figure 1.** Multipole moments of the intrinsic ellipticity autocorrelation functions expanded in the standard Legendre basis, measured from SDSS LRG (left), LOWZ (middle), and CMASS (right) galaxy samples. The upper set shows the II(+) correlation multipoles, ξ+,ℓ, while the lower set shows the II(−) multipoles, ξ−,ℓ, for ℓ = 0 (monopole; circles) and ℓ = 2 (quadrupole; squares). The correlation amplitude for the LRG sample is … view at source ↗

**Figure 2.** Upper panels: similarly to [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Constraints on (bKσ8, σv) from II correlation multipoles of LOWZ sample at 6 ≤ r ≤ 100 h −1 Mpc. The contours show the 68%, 95%, and 99.7% C. L. from inward. The dashed line represents the linear-theory prediction for velocity dispersion. respectively, and given by the inverse Hankel transform, ξ+,ℓ(r) = i ℓ Z k 2dk 2π 2 jℓ(kr)PEE,ℓ(k) , (11) ξe−,L(r) = i L Z k 2dk 2π 2 jL(kr)PeEE,L(k) , (12) where jℓ is the spheric… view at source ↗

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

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