Kavli Affiliate: Blake Sherwin

| First 5 Authors: Noah Sailer, Emmanuel Schaan, Simone Ferraro, Omar Darwish, Blake Sherwin

| Summary:

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 $ell_{text{max,}T}$.

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