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Half-wave-plate non idealities propagated to component separated CMB $B$-modes

Ema Tsang-King-Sang, Josquin Errard, Simon Biquard, Pierre Chanial, Wassim Kabalan, Wuhyun Sohn, Radek Stompor

Abstract

We assess the impact of non-ideal, continuously rotating half-wave plates (HWPs) on cosmic microwave background (CMB) polarization measurements targeting large angular scale signal. Such hardware solutions are used in or planned for multiple modern CMB efforts, both ground-based, for instance, small aperture telescopes of Simons Observatory or satellite borne, such as LiteBIRD. Using a frequency-dependent parametric model based on the Mueller matrix formalism, we characterize the induced mixing of Stokes parameters. Through end-to-end simulations, we propagate these effects from time-ordered data to cosmology via map-making and component-separation stages, quantifying their impact on the $B$-modes power spectrum and the tensor-to-scalar ratio, $r$. Our analysis shows that neglecting the frequency dependence of a three-layer HWP gives rise to significant polarization leakage, biases foreground spectral parameters, and leads to residual contamination in the recovered CMB maps. To mitigate these effects, we investigate multiple analysis strategies progressively incorporating a more complete description of the instrumental response. At the map-making level, this requires generalizing the standard pointing matrix to account for the full time- and frequency-dependent instrumental response. We find that standard HWP models, reduce the biases only down to $r \sim 10^{-2}$, while a more advanced approach based on a generalization of both map-making and component separation, implemented using JAX, can suppress it down to $r \sim 7 \times 10^{-4}$. Finally, we extend this approach to a time-domain component-separation, enabling a statistically consistent treatment of instrumental response in the presence of time-domain features. We demonstrate its feasibility and validate it by performing a full end-to-end analysis, recovering results in good agreement with the map-based ones.

Half-wave-plate non idealities propagated to component separated CMB $B$-modes

Abstract

We assess the impact of non-ideal, continuously rotating half-wave plates (HWPs) on cosmic microwave background (CMB) polarization measurements targeting large angular scale signal. Such hardware solutions are used in or planned for multiple modern CMB efforts, both ground-based, for instance, small aperture telescopes of Simons Observatory or satellite borne, such as LiteBIRD. Using a frequency-dependent parametric model based on the Mueller matrix formalism, we characterize the induced mixing of Stokes parameters. Through end-to-end simulations, we propagate these effects from time-ordered data to cosmology via map-making and component-separation stages, quantifying their impact on the -modes power spectrum and the tensor-to-scalar ratio, . Our analysis shows that neglecting the frequency dependence of a three-layer HWP gives rise to significant polarization leakage, biases foreground spectral parameters, and leads to residual contamination in the recovered CMB maps. To mitigate these effects, we investigate multiple analysis strategies progressively incorporating a more complete description of the instrumental response. At the map-making level, this requires generalizing the standard pointing matrix to account for the full time- and frequency-dependent instrumental response. We find that standard HWP models, reduce the biases only down to , while a more advanced approach based on a generalization of both map-making and component separation, implemented using JAX, can suppress it down to . Finally, we extend this approach to a time-domain component-separation, enabling a statistically consistent treatment of instrumental response in the presence of time-domain features. We demonstrate its feasibility and validate it by performing a full end-to-end analysis, recovering results in good agreement with the map-based ones.
Paper Structure (30 sections, 55 equations, 19 figures, 4 tables)

This paper contains 30 sections, 55 equations, 19 figures, 4 tables.

Table of Contents

  1. Introduction
  2. HWP modelling
  3. Monochromatic HWP
  4. Stacked HWP
  5. Non-ideal HWP
  6. Methodology
  7. Simulation configuration
  8. Input maps
  9. Observing strategy
  10. Map-making procedure
  11. An effective HWP model
  12. A stacked HWP model.
  13. The generalized sky map model.
  14. Map estimation.
  15. Parametric component separation
  16. ...and 15 more sections

Figures (19)

  • Figure 1: Phase shift of the HWP as a function of frequency. The blue line shows the prediction of the non-ideal HWP optical model, while the red curve shows laboratory measurements with $1\sigma$ uncertainties from sugiyama2024simons. The measurements span the MF and UHF frequency ranges and show good agreement with the model across most of the band. A constant offset between the curves is applied since the phase shift is defined only up to an arbitrary additive constant.
  • Figure 2: HWP configuration consisting of a three-layer sapphire stack with Mullite and Duroid anti-reflection coating, following sakaguri2024antireflection.
  • Figure 3: 4$\times$4 Mueller matrix of a 3 layer-stack HWP computed with essinger2013transfer formalism. We observe a frequency-dependent phase shift in the 2$\times$2 central block, along with less efficient modulation compared to the ideal case in $\textit{red dashed lines}$. The analysis reveals an $\mathrm{I} \to \mathrm{QU}$ leakage of 0.05% and $\mathrm{V} \to \mathrm{QU}$ leakage that are both mostly modulated at $2f$.
  • Figure 4: 3$\times$3 Mueller matrix coefficients of a 3 layer-stack HWP computed with essinger2013transfer formalism for different incident angles corresponding to a field-of-view of 17deg
  • Figure 5: Methodology followed in this work to study the impact of HWP-related systematic effects on $B$-modes power spectra and related cosmological parameters.
  • ...and 14 more figures