Spin characterization 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.

Instrumental systematics biases in CMB lensing reconstruction: A simulation-based assessment

“…For example, differential pointing and differential gain systematics can be mitigated by introducing a boresight rotation to the scanning strategy [27]. It may also be possible to mitigate differential pointing effects by knowing analytically how the scanning strategy couples to the pointing signal [81]. To avoid experiment-specific conclusions, in this work we adopted the most conservative approach and did not try to implement scans that are optimized to mitigate systematic effects (as done for several instruments); most of the biases we find are in any case only of marginal importance.…”

“…Our simulated gain variation is not constant in time, so this deprojection model did not mitigate any of the biases we observe. Using different deprojection methods, such as those using template fitting [82] or solving for additional degrees of freedom that mimic leakages that depend on cos (2ψ) and sin (2ψ) may help mitigating gain or beam-related biases [81], at the cost of an increased noise in the final map.…”

The Simons Observatory: gain, bandpass and polarization-angle calibration requirements for B-mode searches

“…Finally, and most importantly, this first study of systematic errors in SO has focused on the impact of instrumental systematics in the form of "averaged" uncertainties in the effective global bandpasses and angles of the final set of frequency maps, and thus, we have not modeled the impact of residual temporal or spatial variations in these effects, which could affect some of the conclusions presented here. Studying this will require the use of TOD simulations or potentially faster analytical methods [46], which we leave for future work.…”

Consequences of constant elevation scans for instrumental systematics in Cosmic Microwave Background Experiments

“…These systematics include pointing errors, anisotropic beam effects, and gain or calibration effects for polarisation detectors. Since the orientation of the focal plane with respect to the sky changes according to how the instrument scans the sky, the contamination caused by these systematics depends on the scan strategy (Wallis et al 2016;McCallum et al 2021a).…”

“…Some systematics, particularly instrumental systematics such as differential gain and pointing errors between differenced detectors, couple to the scan strategy (see e.g. Hu et al (2003); O'Dea et al (2007); Shimon et al (2008); Miller et al (2009); Bock et al (2009); Wallis et al (2016); Hivon et al (2017); McCallum et al (2021a)). This coupling means that knowledge of the scan strategy is required to compute the expected magnitude of the contamination from these systematics, and also that a careful choice of scan strategy may be able to mitigate these systematics.…”