Phys. Rev. D 108, 063518 (2023) - CMB lensing with shear-only reconstruction on the full sky

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CMB lensing with shear-only reconstruction on the full sky

Frank J. Qu, Anthony Challinor, and Blake D. Sherwin

Phys. Rev. D 108, 063518 – Published 18 September 2023

Abstract

Reconstruction of gravitational lensing effects in the CMB from current and upcoming surveys is still dominated by temperature anisotropies. Extragalactic foregrounds in temperature maps can induce significant biases in the lensing power spectrum obtained with the standard quadratic estimators. Techniques such as masking cannot remove these foregrounds fully, and the residuals can still lead to large biases if unaccounted for. In this paper, we study the “shear-only” estimator, an example of a class of geometric methods that suppress extragalactic foreground contamination while making only minimal assumptions about foreground properties. The shear-only estimator has only been formulated in the flat-sky limit and so is not easily applied to wide surveys. Here, we derive the full-sky version of the shear-only estimator and its generalization to an $m = 2$ multipole estimator that has improved performance for lensing reconstruction on smaller scales. The multipole estimator is generally not separable, and so is expensive to compute. We explore separable approximations based on a singular-value decomposition, which allow efficient evaluation of the estimator with real-space methods. Finally, we apply these estimators to simulations that include extragalactic foregrounds and verify their efficacy in suppressing foreground biases.

Received 8 September 2022
Accepted 27 August 2023

DOI:https://doi.org/10.1103/PhysRevD.108.063518

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Cosmic microwave background Cosmology

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Frank J. Qu^1,2,*, Anthony Challinor ^1,3,2,†, and Blake D. Sherwin^1,2,‡

¹DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
²Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge CB3 0HA, United Kingdom
³Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, United Kingdom

^*jq247@cam.ac.uk
^†a.d.challinor@ast.cam.ac.uk
^‡sherwin@damtp.cam.ac.uk

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Vol. 108, Iss. 6 — 15 September 2023

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Figure 1
Lensing convergence reconstructed on the full sky with the shear-only estimator (Eq. (21) applied to a simulated, foreground-free, noisy CMB temperature map. The cross-power spectrum of the reconstructed and input convergence is shown in green, and bandpowers with $Δ L = 60$ of the autopower spectrum of the reconstruction are in red. The latter is corrected for $N^{(0)}$ and $N^{(1)}$ bias terms (shown in blue and orange, dashed, respectively). Both the auto and cross-spectra agree well with the expected power (black).
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Figure 2
Lensing (convergence) reconstruction noise power spectra for the standard quadratic estimator (QE; black), the shear estimator (green), the $m = 2$ symmetric estimator (symmetric $f^{2}$ ; orange), the $m = 2$ asymmetric estimator (asymmetric $f^{2}$ ; blue), and the SVD approximation to the latter (asymmetric $f^{2}$ -SVD; red). The lensing convergence power spectrum is also plotted (dashed black). Note that the convergence spectra are related to the spectra of the lensing potential by, e.g., $N_{L}^{κ κ} = L^{2} (L + 1)^{2} N_{L}^{ϕ ϕ} / 4$ . The survey specifications are the same as in Sec. 2c.
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Figure 3
Power spectra of the tSZ (orange), kSZ (green) and CIB (red) extragalactic foregrounds at 148 GHz from the Websky simulation [27]. The lensed CMB power spectrum is also shown (in blue). The combined total map is matched-filtered and masked for point sources above a flux density of 5 mJy in our tests.
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Figure 4
Relative primary bispectrum bias on the CMB convergence power spectrum due to the combined effect of foregrounds for the standard quadratic estimator (blue), the shear estimator (green) and the hybrid-SVD estimator based on SVD of the asymmetric ${\tilde{f}}_{L, ℓ}^{2}$ response (SVD asymmetric; red). From top to bottom, we vary the maximum CMB temperature multipole used in the reconstruction, $ℓ_{\max} = {3000, 3500, 5000}$ . The shaded bands indicate the $1 σ$ statistical reconstruction error for the different estimators for bandpowers of width $Δ L = 60$ . The bias is well contained within the statistical errors for the shear and hybrid-SVD estimators but there is significant bias in the standard quadratic estimator.
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Figure 5
As Fig. 4 but for the relative trispectrum bias. Similar to the bispectrum biases, the shear and hybrid-SVD estimators suppress the trispectrum bias significantly across most of the lensing multipole range. Note that the bias for the standard quadratic estimator with $ℓ_{\max} = 5000$ is off the scale of the plot. It is worth noting that the trispectrum bias is particularly sensitive to bright tSZ clusters and further improvement can be obtained via cluster masking.
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Physical Review D

covering particles, fields, gravitation, and cosmology

CMB lensing with shear-only reconstruction on the full sky

Frank J. Qu, Anthony Challinor, and Blake D. Sherwin

Phys. Rev. D 108, 063518 – Published 18 September 2023

Abstract

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Physical Review D

covering particles, fields, gravitation, and cosmology

CMB lensing with shear-only reconstruction on the full sky

Frank J. Qu, Anthony Challinor, and Blake D. Sherwin

Phys. Rev. D 108, 063518 – Published 18 September 2023

Abstract

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