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

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.

arXiv commentMinimal revisions - some additional references added, typos fixed, etc. 31 pages, 8 figures, 1 table. Accepted by MNRAS

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• The Simons Observatory: gain, bandpass and polarization-angle calibration requirements for B-mode searches
• The Simons Observatory: Galactic Science Goals and Forecasts
• Instrumental systematics biases in CMB lensing reconstruction: a simulation-based assessment
• A numerical study of observational systematic errors in lensing analysis of CMB polarization
• Blind Map Level Systematics Cleaning: A Quadratic Estimator Approach
• Consequences of constant elevation scans for instrumental systematics in Cosmic Microwave Background Experiments
• Multi-dimensional optimisation of the scanning strategy for the LiteBIRD space mission
• Spin-based removal of instrumental systematics in 21cm intensity mapping surveys
• Fast map-based simulations of systematics in CMB surveys including effects of the scanning strategy