Lower bias, lower noise CMB lensing with foreground-hardened estimators

TL;DR

This paper introduces a bias-hardening technique for CMB lensing estimators that effectively reduces foreground bias and noise, significantly improving the statistical power of lensing measurements in temperature maps.

Contribution

The authors develop a simple bias hardening method that deprojects extragalactic foregrounds, enhancing lensing reconstruction accuracy and extending usable multipole range for future experiments.

Findings

Bias hardening reduces foreground bias in lensing estimates.

Method increases statistical power by ~50% over standard estimators.

Outperforms shear-only and standard quadratic estimators in simulations.

Abstract

Extragalactic foregrounds in temperature maps of the Cosmic Microwave Background (CMB) severely limit the ability of standard estimators to reconstruct the weak lensing potential. These foregrounds are not fully removable by multi-frequency cleaning or masking and can lead to large biases if not properly accounted for. For foregrounds made of a number of unclustered point sources, an estimator for the source amplitude can be derived and deprojected, removing any bias to the lensing reconstruction. We show with simulations that all of the extragalactic foregrounds in temperature can be approximated by a collection of sources with identical profiles, and that a simple bias hardening technique is effective at reducing any bias to lensing, at a minimal noise cost. We compare the performance and bias to other methods such as "shear-only" reconstruction, and discuss how to jointly deproject any arbitrary number of foregrounds, each with an arbitrary profile. In particular, for a Simons Observatory-like experiment foreground-hardened estimators allow us to extend the maximum multipole used in the reconstruction, increasing the overall statistical power by $\sim 50\%$ over the standard quadratic estimator, both in auto and cross-correlation. We conclude that source hardening outperforms the standard lensing quadratic estimator both in auto and cross-correlation, and in terms of lensing signal-to-noise and foreground bias.