Position-space curved-sky anisotropy quadratic estimation

TL;DR

This paper provides detailed calculations and derivations for curved-sky quadratic estimators used in analyzing CMB lensing data, enhancing the Planck 2018 pipeline with new analytic tools.

Contribution

It introduces analytic calculations of estimator responses, noise biases, and derives optimal joint estimators for anisotropy of arbitrary spin in position space.

Findings

Analytic expressions for estimator responses and noise biases.

Derivation of optimal joint gradient and curl mode estimators.

Enhanced tools for analyzing CMB lensing anisotropies.

Abstract

This document supplements the release of the Planck 2018 CMB lensing pipeline, now made publicly available. It collects calculations relevant to curved-sky separable quadratic estimators in the spin-weight, position-space correlation function formalism, including analytic calculations of estimator responses and Gaussian noise biases between arbitrary pairs of quadratic estimators. It also contains the derivation of optimal, joint gradient and curl mode quadratic estimators for parametrized anisotropy of arbitrary spin.