Spin characterisation of systematics in CMB surveys -- a comprehensive formalism

TL;DR

This paper introduces a comprehensive formalism to characterize and mitigate systematic effects, especially spin-related leakage, in CMB B-mode polarization surveys, enhancing the accuracy of primordial gravitational wave detection.

Contribution

It provides a general, versatile formalism for analyzing spin-related systematics in CMB surveys, including a new cross-term in the power spectrum and methods for systematic removal during map-making.

Findings

Identified a new cross-term between systematics and sky signals in power spectra.

Validated the formalism with simulations of differential gain and pointing systematics.

Demonstrated potential to remove spin-coupled systematics during map-making.

Abstract

The CMB $B$-mode polarisation signal -- both the primordial gravitational wave signature and the signal sourced by lensing -- is subject to many contaminants from systematic effects. Of particular concern are systematics that result in mixing of signals of different ``spin'', particularly leakage from the much larger spin-0 intensity signal to the spin-2 polarisation signal. We present a general formalism, which can be applied to arbitrary focal plane setups, that characterises signals in terms of their spin. We provide general expressions to describe how spin-coupled signals observed by the detectors manifest at map-level, in the harmonic domain, and in the power spectra, focusing on the polarisation spectra -- the signals of interest for upcoming CMB surveys. We demonstrate the presence of a previously unidentified cross-term between the systematic and the intrinsic sky signal in the power spectrum, which in some cases can be the dominant source of contamination. The formalism is not restricted to intensity to polarisation leakage but provides a complete elucidation of all leakage including polarisation mixing, and applies to both full and partial (masked) sky surveys, thus covering space-based, balloon-borne, and ground-based experiments. Using a pair-differenced setup, we demonstrate the formalism by using it to completely characterise the effects of differential gain and pointing systematics, incorporating both intensity leakage and polarisation mixing. We validate our results with full time ordered data simulations. Finally, we show in an Appendix that an extension of simple binning map-making to include additional spin information is capable of removing spin-coupled systematics during the map-making process.