Optimal multifrequency weighting for CMB lensing

Abstract

Extragalactic foregrounds in Cosmic Microwave Background (CMB) temperature maps lead to significant biases in CMB lensing reconstruction if not properly accounted for. Combinations of multi-frequency data have been used to minimize the overall map variance (internal linear combination, or ILC), or specifically null a given foreground, but these are not tailored to CMB lensing. In this paper, we derive an optimal multi-frequency combination to jointly minimize CMB lensing noise and bias. We focus on the standard lensing quadratic estimator, as well as the "shear-only" and source-hardened estimators, whose responses to foregrounds differ. We show that an optimal multi-frequency combination is a compromise between the ILC and joint deprojection, which nulls the thermal Sunyaev-Zel'dovich (tSZ) and Cosmic Infrared Background (CIB) contributions. In particular, for a Simons Observatory-like experiment with ${\ell }_{\text{max},T}=3000$, we find that profile hardening alone (with the standard ILC) reduces the bias to the lensing power amplitude by $40\%$, at a $20\%$ cost in noise, while the bias to the cross-correlation with a LSST-like sample is reduced by nearly an order of magnitude at a $10\%$ noise cost, relative to the standard quadratic estimator. With a small amount of joint deprojection the bias to the profile hardened estimator can be further reduced to less than half the statistical uncertainty on the respective amplitudes, at a $20\%$ and $5\%$ noise cost for the auto- and cross-correlation respectively, relative to the profile hardened estimator with the standard ILC weights. Finally, we explore possible improvements with more aggressive masking and varying ${\ell }_{\text{max,}T}$.

arXiv commentpublished in PRD

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• Cosmological Analysis of Three-Dimensional BOSS Galaxy Clustering and Planck CMB Lensing Cross Correlations via Lagrangian Perturbation Theory
• Foreground-immune CMB lensing reconstruction with polarization
• The impact of extragalactic foregrounds on internal delensing of CMB B-mode polarization
• Constraining the galaxy-halo connection of infrared-selected unWISE galaxies with galaxy clustering and galaxy-CMB lensing power spectra
• CMB lensing with shear-only reconstruction on the full sky
• Constraining the physics of star formation from CIB-cosmic shear cross-correlations
• The Bias to Cosmic Microwave Background Lensing Reconstruction from the Kinematic Sunyaev-Zel'dovich Effect at Reionization