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Intrinsic alignment-lensing interference as a contaminant of cosmic shear

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Christopher M. Hirata, Uros Seljak

Astrophysics · Submitted 10 Jun 2004 · 62 references

Pith's verdict: The paper that put the GI term on the map: the structural argument is right and has held up for twenty years, and the authors are more candid about the normalization than the abstract lets on.

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arXiv IDastro-ph/0406275 (version 3)
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CitationChristopher M. Hirata, Uros Seljak. "Intrinsic alignment-lensing interference as a contaminant of cosmic shear." arXiv:astro-ph/0406275 (2004). https://pith.science/paper/HWAQYAXM
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The paper

The paper claims

Cosmic shear surveys may be contaminated by a correlation between the intrinsic shapes of nearby galaxies and the lensing of distant ones, an effect that survives the usual redshift cuts.

The reading

Weak gravitational lensing measures cosmology by averaging the shapes of millions of galaxies, and the standard worry is that galaxies are born with intrinsic alignments that mimic lensing. The usual defence is to throw away pairs of galaxies at similar redshifts, on the assumption that widely separated galaxies have unrelated intrinsic shapes. This paper argues that assumption is wrong: the same tidal field that stretches a nearby galaxy also lenses the more distant one behind it, so the intrinsic shear and the gravitational shear are correlated rather than independent. The authors compute this gravitational-intrinsic (GI) interference term for two simple alignment models and show that, in the linear model, it can be an order of magnitude larger than the intrinsic-intrinsic term it was supposed to be safely quarantined from. If the estimate holds, a single broad redshift bin could lose of order 10% of its lensing power at $z_s=1$ and 30% at $z_s=0.5$, which matters for any survey aiming at percent-level cosmology.

What carries the argument

The load-bearing object is the GI cross-spectrum $C_ell^{EE,GI}(alpha,beta)$, built from the three-dimensional density-intrinsic-shear cross-spectrum $P_{delta,tilde{gamma}_I}(k)$ and projected along the line of sight with the lensing window of one redshift slice and the galaxy distribution of the other. The sign and amplitude come from the linear alignment model, in which intrinsic shear is proportional to the second derivatives of the smoothed primordial potential, $gamma_I = -frac{C_1}{4pi G}(nabla_x^2-nabla_y^2,, 2nabla_xnabla_y)S[Psi_P]$, which yields $P_{delta,tilde{gamma}_I}(k) = -C_1 bar{rho}bar{D}a^2 P_delta^{lin}(k)$ and a correlation coefficient between density and intrinsic shear of order unity. The quadratic model, $gamma_I = C_2(T_{xmu}^2 - T_{ymu}^2,, 2T_{xmu}T_{ymu})$, gives zero cross-spectrum at leading order because the relevant third moments of a Gaussian density field vanish. The amplitude $C_1$ is fixed by matching the SuperCOSMOS ellipticity variance measured by Brown et al.

Extended reading notes

Core claim

The paper's claim is that gravitational lensing shear and intrinsic galaxy shear need not be statistically independent. A foreground galaxy's ellipticity is set by the tidal field around it; that same tidal field contributes to the lensing of a background galaxy further along the line of sight. The cross term this produces, $C_ell^{EE,GI}$, is computed here by Limber projection of the density-intrinsic-shear cross-spectrum $P_{delta,tilde{gamma}_I}(k)$, and it has three properties that make it awkward. First, it is linear in the intrinsic alignment amplitude rather than quadratic, so it can exceed the usual $II$ contamination by more than an order of magnitude for broad redshift distributions. Second, it requires radial separation between the two galaxies, so it is not removed by rejecting close pairs in photometric redshift. Third, it contributes only to E-modes, so the B-mode power spectrum, widely used as the null test for intrinsic alignments, is blind to it: the authors quote a case where the E-mode change from intrinsic alignments exceeds the B-mode by two orders of magnitude. For a simple quadratic alignment model of the kind motivated by tidal torque theory, the GI term vanishes identically under Gaussian density fields, so the size of the effect is strongly model-dependent.

Load-bearing premise

The size of the effect rests on normalizing the linear alignment amplitude to the SuperCOSMOS ellipticity variance, a signal the authors themselves say is an order of magnitude above the lensing prediction and may be dominated by observational systematics, and whose sign cannot be determined from a variance at all.

Editorial extensions

If this is right

  • Cross-correlating shear in widely separated photometric redshift bins does not remove intrinsic alignment contamination, because the GI term grows precisely with radial separation.
  • A clean B-mode spectrum is not evidence that intrinsic alignments are absent: the GI term is pure E-mode, so the standard null test can pass while the E-mode lensing amplitude is suppressed.
  • For a single broad redshift bin the lensing power can be suppressed by roughly 10% at $z_s=1$ and 30% at $z_s=0.5$, which propagates into inferred values of $sigma_8$ and the dark energy equation of state.
  • Two routes to constrain the effect are proposed: measuring the density-shear correlation $Delta gamma(r)$ on large transverse separations in a wide shallow survey, and projecting out the known redshift scaling of the GI signal in narrow-bin tomography.

Reading between the lines

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

  • The manuscript carries a correction notice dated July 2010 thanking several named colleagues for pointing out an error in the original version, so the numbers quoted here should be read as the corrected ones rather than the 2004 values.
  • If the linear model describes early-type galaxies while spirals follow the quadratic model, splitting the source sample by morphology or colour could reduce the GI term without discarding data, which is a cheap test the paper does not develop.
  • The same interference should appear wherever galaxy shear is cross-correlated with a lensing field sourced by the same foreground matter, including cosmic microwave background lensing crossed with low-redshift galaxy shapes.
  • The sign of $C_1$ is undetermined by an ellipticity variance and is chosen positive on physical grounds; a measurement of the sign of $Delta gamma(r)$ at tens of comoving megaparsecs would decide whether the effect suppresses or enhances the lensing power.
Original abstract

Cosmic shear surveys have great promise as tools for precision cosmology, but can be subject to systematic errors including intrinsic ellipticity correlations of the source galaxies. The intrinsic alignments are believed to be small for deep surveys, but this is based on intrinsic and lensing distortions being uncorrelated. Here we show that the gravitational lensing shear and intrinsic shear need not be independent: correlations between the tidal field and the intrinsic shear cause the intrinsic shear of nearby galaxies to be correlated with the gravitational shear acting on more distant galaxies. We estimate the magnitude of this effect for two simple intrinsic alignment models: one in which the galaxy ellipticity is linearly related to the tidal field, and one in which it is quadratic in the tidal field as suggested by tidal torque theory. The first model predicts a gravitational-intrinsic (GI) correlation that can be much greater than the intrinsic-intrinsic (II) correlation for broad redshift distributions, and that remains when galaxies pairs at similar redshifts are rejected. The second model, in its simplest form, predicts no gravitational-intrinsic correlation. In the first model and assuming a normalization consistent with recently claimed detections of intrinsic correlations we find that the GI correlation term can exceed the usual II term by >1 order of magnitude and the intrinsic correlation induced B-mode by 2 orders of magnitude. These interference effects can suppress the lensing power spectrum for a single broad redshift bin by of order ~10% at z_s=1 and ~30% at z_s=0.5.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,490 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.49 · human participants 0.01 · controlled comparison 0.13 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.82 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

Cosmic shear surveys have great promise as tools for precision cosmology, but can be subject to systematic errors including intrinsic ellipticity correlations of the source galaxies. The intrinsic alignments are believed to be small for deep surveys, but this is based on intrinsic and lensing distortions being uncorrelated. Here we show that the gravitational lensing shear and intrinsic shear need not be independent: correlations between the tidal field and the intrinsic shear cause the intrinsic shear of nearby galaxies to be correlated with the gravitational shear acting on more distant galaxies. We estimate the magnitude of this effect for two simple intrinsic alignment models: one in which the galaxy ellipticity is linearly related to the tidal field, and one in which it is quadratic in the tidal field as suggested by tidal torque theory. The first model predicts a gravitational-intrinsic (GI) correlation that can be much greater than the intrinsic-intrinsic (II) correlation for broad redshift distributions, and that remains when galaxies pairs at similar redshifts are rejected. The second model, in its simplest form, predicts no gravitational-intrinsic correlation. In the first model and assuming a normalization consistent with recently claimed detections of intrinsic correlations we find that the GI correlation term can exceed the usual II term by >1 order of magnitude and the intrinsic correlation induced B-mode by 2 orders of magnitude. These interference effects can suppress the lensing power spectrum for a single broad redshift bin by of order ~10% at z_s=1 and ~30% at z_s=0.5.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Cosmic shear surveys have great promise as tools for precision cosmology, but can be subject to systematic errors including intrinsic ellipticity correlations of the source galaxies. background 1.00 0.04 0.03 hedged possibility 0.60
s1 The intrinsic alignments are believed to be small for deep surveys, but this is based on intrinsic and lensing distortions being uncorrelated. gap 0.53 0.04 0.04 hedged possibility 0.73
s2 Here we show that the gravitational lensing shear and intrinsic shear need not be independent: correlations between the tidal field and the intrinsic shear cause the intrinsic shear of nearby galaxies to be correlated with the gravitational shear acting on more distant galaxies. contribution 0.75 0.77 0.82 asserted 0.94
s3 We estimate the magnitude of this effect for two simple intrinsic alignment models: one in which the galaxy ellipticity is linearly related to the tidal field, and one in which it is quadratic in the tidal field as suggested by tidal torque theory. method 0.90 0.90 0.05 asserted 0.91
s4 The first model predicts a gravitational-intrinsic (GI) correlation that can be much greater than the intrinsic-intrinsic (II) correlation for broad redshift distributions, and that remains when galaxies pairs at similar redshifts are rejected. result 1.00 0.88 0.33 asserted 0.85
s5 The second model, in its simplest form, predicts no gravitational-intrinsic correlation. result 1.00 0.82 0.06 asserted 0.78
s6 In the first model and assuming a normalization consistent with recently claimed detections of intrinsic correlations we find that the GI correlation term can exceed the usual II term by >1 order of magnitude and the intrinsic correlation induced B-mode by 2 orders of magnitude. result 1.00 0.85 0.22 asserted 0.92
s7 These interference effects can suppress the lensing power spectrum for a single broad redshift bin by of order ~10% at z_s=1 and ~30% at z_s=0.5. result 0.98 0.88 0.24 hedged possibility 0.56

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.85.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. FIG. 1: The effect of the density-intrinsic shear correlatio
Figure 2. FIG. 2: The gravitational (
Figure 3. FIG. 3: The intrinsic shear statistic ∆

Figures reproduced from arXiv:astro-ph/0406275 by the authors.

References
How later papers used it

270 later papers cite it

Evidence: substantial. 262 of the citing papers share no author with it, and 91 of those carry a confident label from Pith's citation classifier.

Pith read 39 of the 471 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 15 of 82 papers with this label · 1 by the same authors

By the same authors

Cites it as support 1 of 5 papers with this label
How the literature uses it

103 arXiv papers cite this in 184 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 93 sentences without a confident label

Contests it 1 paper
Builds on it 2 papers
  • This model is a natural extension to the nonlinear tidal alignment model described in [ref] and incorporates second-order contributions from the tidal torquing model [ref] , including mixed terms between galaxies with alignments sourced by different mechanisms.

    Beyond linear galaxy alignments · Introduction · 1.00

  • In [ref] , we generalize FAST-PT to “tensor” quantities (broadly defined as those that with explicit dependence on the line-of-sight), including those relevant to the intrinsic alignments of galaxies (e.g. [ref] ), redshift space distortions, and CMB anisotropies.

    FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory · Summary · 0.80

Uses its method or tool 26 papers
Compares with it 2 papers
Cites it as support 2 papers
Cites it as background 41 papers

Discussion

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